Review #2. Statistics

Size: px
Start display at page:

Download "Review #2. Statistics"

Transcription

1 Review #2 Statistics Find the mean of the given probability distribution. 1) x P(x) A) 1.64 B) 1.45 C) 1.55 D) ) The number of golf balls ordered by customers of a pro shop has the following probability distribution. x p(x) A) 9 B) 8.22 C) 6.63 D) 9.3 3) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are , , , , and , respectively. Round answer to the nearest hundredth. A) 1.11 B) 0.56 C) 0.46 D) ) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.50, 0.38, 0.11, and 0.01, respectively. A) 0.63 B) 0.25 C) 1.13 D) 1.50 Solve the problem. 5) Find the variance for the given probability distribution. x P(x) A) 7.43 B) 2.63 C) 2.46 D) ) Find the variance for the given probability distribution. x P(x) A) 2.85 B) 2.44 C) 1.56 D) 1.69

2 7) In a certain town, 60% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. Find the variance for the probability distribution. x P(x) A) 0.84 B) 0.98 C) 6.72 D) ) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are , , , , and , respectively. Find the variance for the probability distribution. A) 0.77 B) 0.59 C) 1.11 D) ) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are , , , , and , respectively. Find the standard deviation for the probability distribution. A) 0.56 B) 0.76 C) 0.63 D) ) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.52, 0.40, 0.07, and 0.01, respectively. Find the standard deviation for the probability distribution. Round answer to the nearest hundredth. A) 0.88 B) 0.45 C) 0.67 D) ) In a game, you have a 1/42 probability of winning $67 and a 41/42 probability of losing $7. What is your expected value? A) -$5.24 B) $8.43 C) $1.60 D) -$ ) A contractor is considering a sale that promises a profit of $23,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $13,000 with a probability of 0.3. What is the expected profit? A) $12,200 B) $25,200 C) $16,100 D) $10,000 13) Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected value? A) -$0.50 B) -$1.00 C) -$0.40 D) $0.00 Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 14) Rolling a single die 19 times, keeping track of the numbers that are rolled. A) Not binomial: there are too many trials. B) Procedure results in a binomial distribution. C) Not binomial: there are more than two outcomes for each trial. D) Not binomial: the trials are not independent. 15) Rolling a single die 46 times, keeping track of the ʺfivesʺ rolled. A) Not binomial: the trials are not independent. B) Procedure results in a binomial distribution. C) Not binomial: there are too many trials. D) Not binomial: there are more than two outcomes for each trial.

3 Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. 16) n = 4, x = 3, p = 1 6 A) B) C) D) ) n = 6, x = 3, p = 1 6 A) B) C) D) ) n = 10, x = 2, p = 1 3 A) B) C) D) ) n = 5, x = 2, p = 0.70 A) B) C) D) ) n = 30, x = 12, p = 0.20 A) B) C) D) ) n =12, x = 5, p = 0.25 A) B) C) D) Find the indicated probability. 22) A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? A) B) C) D) ) In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority? A) B) C) D) ) Find the probability of at least 2 girls in 10 births. Assume that male and female births are equally likely and that the births are independent events. A) B) C) D) ) An airline estimates that 98% of people booked on their flights actually show up. If the airline books 76 people on a flight for which the maximum number is 74, what is the probability that the number of people who show up will exceed the capacity of the plane? A) B) C) D) Find the mean, μ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. 26) n = 33; p =.2 A) μ = 6.6 B) μ = 6.1 C) μ = 7.3 D) μ = ) n = 20; p = 3/5 A) μ = 12.7 B) μ = 12.0 C) μ = 12.3 D) μ = 11.5

4 28) n = 665; p =.7 A) μ = B) μ = C) μ = D) μ = Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. 29) n = 36; p =.2 A) σ = 2.40 B) σ = C) σ = 6.52 D) σ = ) n = 25; p = 3/5 A) σ = 5.72 B) σ = 2.45 C) σ = 6.57 D) σ = ) n = 574; p =.7 A) σ = B) σ = C) σ = 8.57 D) σ = ) n = 2661; p =.63 A) σ = B) σ = C) σ = D) σ = Use the given values of n and p to find the minimum usual value μ- 2σ and the maximum usual value μ + 2σ. 33) n = 94, p = 0.20 A) Minimum: ; maximum: B) Minimum: 11.04; maximum: C) Minimum: 14.92; maximum: D) Minimum: 26.56; maximum: ) n = 189, p = 0.13 A) Minimum: ; maximum: B) Minimum: 33.82; maximum: C) Minimum: 19.95; maximum: D) Minimum: 15.32; maximum: ) n = 1100, p = 0.84 A) Minimum: ; maximum: B) Minimum: 906.8; maximum: C) Minimum: ; maximum: D) Minimum: ; maximum: ) n = 1104, p = 0.93 A) Minimum: ; maximum: B) Minimum: ; maximum: C) Minimum: ; maximum: D) Minimum: ; maximum: Solve the problem. 37) According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16. A) 4.00 B) 0.22 C) 3.52 D) ) A die is rolled 7 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos. A) 2.33 B) 1.17 C) 5.83 D) ) On a multiple choice test with 11 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers. A) 5.5 B) 8.3 C) 2.8 D) 3.7

5 Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than μ - 2σ or greater than μ + 2σ. 40) A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 687 consumers who recognize the Dull Computer Company name? A) Yes B) No 41) A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 481 consumers who recognize the Dull Computer Company name? A) Yes B) No Using the following uniform density curve, answer the question. 42) What is the probability that the random variable has a value greater than 3? A) B) C) D) ) What is the probability that the random variable has a value greater than 5.3? A) B) C) D) ) What is the probability that the random variable has a value less than 6? A) B) C) D) If Z is a standard normal variable, find the probability. 45) The probability that Z lies between 0 and 3.01 A) B) C) D) ) The probability that Z lies between and 0 A) B) C) D) ) The probability that Z is less than 1.13 A) B) C) D) ) The probability that Z lies between and A) B) C) D) ) The probability that Z lies between 0.7 and 1.98 A) B) C) D) ) The probability that Z lies between and 0.55 A) B) C) D) ) The probability that Z is greater than A) B) C) D)

6 52) P(Z > 0.59) A) B) C) D) ) P(Z < 0.97) A) B) C) D) ) P(-0.73 < Z < 2.27) A) B) C) 1.54 D) The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0 C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0 C (denoted by negative numbers) and some give readings above 0 C (denoted by positive numbers). Assume that the mean reading is 0 C and the standard deviation of the readings is 1.00 C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. 55) Find P40, the 40th percentile. A) B) 0.25 C) D) ) Find Q3, the third quartile. A) -1.3 B) 0.82 C) 0.53 D) ) If 9% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others. A) 1.39 B) 1.26 C) 1.34 D) 1.45 Assume that X has a normal distribution, and find the indicated probability. 58) The mean is μ = 60.0 and the standard deviation is σ = 4.0. Find the probability that X is less than A) B) C) D) ) The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than A) B) C) D) ) The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than A) B) C) D) ) The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is between 14.3 and A) B) C) D) Solve the problem. 62) In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kwh and a standard deviation of 218 kwh. Find P45, which is the consumption level separating the bottom 45% from the top 55%. A) B) C) D)

7 63) Scores on a test are normally distributed with a mean of 65.3 and a standard deviation of Find P81, which separates the bottom 81% from the top 19%. A) 0.88 B) 74.4 C) 68.3 D) ) A bankʹs loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. Find P60, the score which separates the lower 60% from the top 40%. A) B) C) D) ) Scores on an English test are normally distributed with a mean of 33.8 and a standard deviation of 8.5. Find the score that separates the top 59% from the bottom 41% A) 31.8 B) 28.8 C) 38.8 D) 35.8 Find the indicated probability. 66) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches? A) 97.72% B) 37.45% C) 2.28% D) 47.72% 67) The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month? A) 9.18% B) 90.82% C) 35.31% D) 40.82% 68) The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week? A) B) C) D) Find the margin of error for the 95% confidence interval used to estimate the population proportion. 69) n = 169, x = 107 A) B) C) D) ) n = 230, x = 90 A) B) C) D) ) In a survey of 4100 T.V. viewers, 20% said they watch network news programs. A) B) C) D) Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 72) n = 58, x = 28; 95 percent A) < p < B) < p < C) < p < D) < p < ) n = 84, x = 37; 98 percent A) < p < B) < p < C) < p < D) < p < ) n = 102, x = 52; 88 percent A) < p < B) < p < C) < p < D) < p < ) n = 133, x = 82; 90 percent A) < p < B) < p < C) < p < D) < p < 0.688

8 76) n = 182, x = 135; 95 percent A) < p < B) < p < C) < p < D) < p < Find the minimum sample size you should use to assure that your estimate of p^ will be within the required margin of error around the population p. 77) Margin of error: 0.01; confidence level: 95%; from a prior study, p^ is estimated by the decimal equivalent of 69%. A) 7396 B) 14,184 C) 26,507 D) ) Margin of error: 0.04; confidence level: 99%; from a prior study, p^ is estimated by 0.08 A) 306 B) 12 C) 367 D) ) Margin of error: 0.04; confidence level: 95%; from a prior study, p^ is estimated by the decimal equivalent of 92%. A) 531 B) 177 C) 157 D) 7 Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 80) A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval. A) < p < B) < p < C) < p < D) < p < ) Of 346 items tested, 12 are found to be defective. Construct the 98% confidence interval for the proportion of all such items that are defective. A) < p < B) < p < C) < p < D) < p < Use the confidence level and sample data to find the margin of error E. 82) Weights of eggs: 95% confidence; n = 47, x = 1.44 oz, σ = 0.39 oz A) 6.86 oz B) 0.09 oz C) 0.11 oz D) 0.02 oz 83) Replacement times for washing machines: 90% confidence; n = 36, x = 10.0 years, σ = 2.1 years A) 0.6 years B) 6.0 years C) 0.1 years D) 0.4 years 84) College studentsʹ annual earnings: 99% confidence; n = 71, x = $3660, σ = $879 A) $8 B) $1118 C) $243 D) $269 Use the confidence level and sample data to find a confidence interval for estimating the population μ. 85) Test scores: n = 109, x = 79.1, σ = 6.9; 99 percent A) 78.0 < μ < 80.2 B) 77.8 < μ < 80.4 C) 77.6 < μ < 80.6 D) 77.4 < μ < ) Test scores: n = 71, x = 41.8, σ = 7.2; 98 percent A) 39.8 < μ < 43.8 B) 40.4 < μ < 43.2 C) 39.6 < μ < 44.0 D) 40.1 < μ < ) A random sample of 79 light bulbs had a mean life of x = 400 hours with a standard deviation of σ = 28 hours. Construct a 90 percent confidence interval for the mean life, μ, of all light bulbs of this type. A) 392 < μ < 408 B) 394 < μ < 406 C) 393 < μ < 407 D) 395 < μ < 405

9 88) A random sample of 144 full-grown lobsters had a mean weight of 18 ounces and a standard deviation of 2.9 ounces. Construct a 98 percent confidence interval for the population mean μ. A) 16 < μ < 18 B) 17 < μ < 20 C) 17 < μ < 19 D) 18 < μ < 20 Use the margin of error, confidence level, and standard deviation σto find the minimum sample size required to estimate an unknown population mean μ. 89) Margin of error: $121, confidence level: 95%, σ = $528 A) 2 B) 4 C) 74 D) 64 90) Margin of error: $126, confidence level: 99%, σ = $534 A) 120 B) 105,268 C) 61 D) 69 Find the margin of error. _ 91) 95% confidence interval; n = 91 ; x = 72, s = 11.4 A) 2.37 B) 4.57 C) 2.03 D) 2.13 _ 92) 99% confidence interval; n = 201; x = 217; s = 34 A) 6.2 B) 5.6 C) 4.7 D) 8.4 _ 93) 95% confidence interval; n = 21; x = 0.44; s = 0.44 A) B) C) D) Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. 94) n = 10, x = 12.8, s = 4.9, 95 percent A) 9.29 < μ < B) 9.31 < μ < C) 9.35 < μ < D) 9.96 < μ < ) n = 12, x = 19.1, s = 5.0, 99 percent A) < μ < B) < μ < C) < μ < D) < μ < ) n = 30, x = 86.5, s = 10.3, 90 percent A) < μ < B) < μ < C) < μ < D) < μ < ) The principal randomly selected six students to take an aptitude test. Their scores were: Determine a 90 percent confidence interval for the mean score for all students. A) < μ < B) < μ < C) < μ < D) < μ < Solve the problem. 98) Find the critical value χ 2 R corresponding to a sample size of 19 and a confidence level of 99 percent. A) B) C) D) 6.265

10 99) Find the critical value χ 2 L corresponding to a sample size of 9 and a confidence level of 90 percent. A) B) C) D) Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. 100) Weights of men: 90% confidence; n = 14, x = lb, s = 12.6 lb A) 9.6 lb < σ < 18.7 lb B) 10.2 lb < σ < 2.7 lb C) 9.3 lb < σ < 17.7 lb D) 9.9 lb < σ < 16.3 lb 101) Weights of eggs: 95% confidence; n = 22, x = 1.77 oz, s = 0.47 oz A) 0.36 oz < σ < 0.67 oz B) 0.37 oz < σ < 0.61 oz C) 0.38 oz < σ < 0.63 oz D) 0.36 oz < σ < 0.65 oz 102) College studentsʹ annual earnings: 98% confidence; n = 9, x = $3262, s = $836 A) $658 < σ < $1091 B) $508 < σ < $1636 C) $528 < σ < $1843 D) $565 < σ < $1602 Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form. Use the correct symbol (μ, p, σ )for the indicated parameter. 103) An entomologist writes an article in a scientific journal which claims that fewer than 11 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light. A) H0: p < B) H0: p = C) H0: p > D) H0: p = H1: p H1: p < H1: p H1: p > ) Carter Motor Company claims that its new sedan, the Libra, will average better than 30 miles per gallon in the city. Use μ, the true average mileage of the Libra. A) H0: μ < 30 H1: μ 30 B) H0: μ > 30 H1: μ 30 C) H0: μ = 30 H1: μ < 30 D) H0: μ = 30 H1: μ > ) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 2 in every one thousand. A) H0: p < H1: p B) H0: p = H1: p < C) H0: p = H1: p > D) H0: p > H1: p Identify the null hypothesis, alternative hypothesis, test statistic, P -value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. 106) A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the 0.01 level of significance, test the managerʹs claim. 107) A supplier of 3.5ʺ disks claims that no more than 1% of the disks are defective. In a random sample of 600 disks, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplierʹs claim that no more than 1% are defective. 108) According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 45% who would vote for the incumbent, test the claim that the actual percentage is 53%. Use a 0.10 significance level.

11 Find the P-value for the indicated hypothesis test. 109) A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the schoolʹs students, 32% of them plan to go into general practice. Find the P-value for a test of the schoolʹs claim. A) B) C) D) ) In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from asthma. Find the P-value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%. A) B) C) D) ) In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%. A) B) C) D) Identify the null hypothesis, alternative hypothesis, test statistic, P -value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. 112) Various temperature measurements are recorded at different times for a particular city. The mean of 20 C is obtained for 40 temperatures on 40 different days. Assuming that σ = 1.5 C, test the claim that the population mean is 23 C. Use a 0.05 significance level. 113) The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of lb. Assuming that σ is known to be lb, use a 0.10 significance level to test the claim that the population mean of all such employees weights is less than 200 lb. Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. 114) Claim: μ = 959. Sample data: n = 25, x = 951, s = 25. The sample data appear to come from a normally distributed population with σ = 28. A) Student t B) Neither C) Normal 115) Claim: μ = 119. Sample data: n = 15, x = 103, s = The sample data appear to come from a normally distributed population with unknown μ and σ. A) Normal B) Student t C) Neither 116) Claim: μ = 78. Sample data: n = 24, x = 101, s = The sample data appear to come from a population with a distribution that is very far from normal, and σ is unknown. A) Neither B) Normal C) Student t Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion. 117) Test the claim that for the population of female college students, the mean weight is given by μ = 132 lb. Sample data are summarized as n = 20, x = 137 lb, and s = 14.2 lb. Use a significance level of α = ) Test the claim that for the adult population of one town, the mean annual salary is given by μ = $30,000. Sample data are summarized as n = 17, x = $22,298, and s = $14,200. Use a significance level of α = 0.05.

12 119) Test the claim that the mean age of the prison population in one city is less than 26 years. Sample data are summarized as n = 25, x = 24.4 years, and s = 9.2 years. Use a significance level of α = Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution. 120) Use a significance level of α = 0.05 to test the claim that μ The sample data consists of 15 scores for which x = 39.7 and s = ) A test of sobriety involves measuring the subjectʹs motor skills. Twenty randomly selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of 3.7. At the 0.01 level of significance, test the claim that the true mean score for all sober subjects is equal to ) A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 11 such cases from court files and finds that x = 20.5 months and s = 7.9 months. Test the null hypothesis that μ = 18.7 at the 0.05 significance level. Find the critical value or values of x2 based on the given information. 123) H0: σ = 8.0 n = 10 α = 0.01 A) 2.088, B) 1.735, C) D) ) H1: σ > 3.5 n = 14 α = 0.05 A) B) C) D) ) H1: σ < 0.14 n = 23 α = 0.10 A) B) C) D)

13 Answer Key Testname: REVIEW 2 1) C 2) D 3) B 4) A 5) C 6) A 7) D 8) B 9) C 10) C 11) A 12) A 13) A 14) C 15) B 16) B 17) A 18) A 19) C 20) B 21) B 22) A 23) B 24) D 25) D 26) A 27) B 28) A 29) A 30) B 31) A 32) D 33) B 34) D 35) C 36) C 37) C 38) B 39) C 40) A 41) A 42) B 43) A 44) C 45) D 46) B 47) B 48) D 49) A 50) D 51) A 52) C 53) C 54) B 55) A 56) D 57) C 58) D 59) A 60) D 61) D 62) B 63) B 64) C 65) A 66) C 67) A 68) A 69) A 70) A 71) D 72) A 73) A 74) B 75) C 76) D 77) D 78) A 79) B 80) C 81) A 82) C 83) A 84) D 85) D 86) A 87) D 88) C 89) C 90) A 91) A 92) A 93) B 94) A 95) A 96) C 97) C 98) B 99) A 100) A 101) A 102) C

14 Answer Key Testname: REVIEW 2 103) B 104) D 105) B 106) H0: p = H1: p > Test statistic: z = P-value: p = Critical value: z = Fail to reject null hypothesis. There is not sufficient evidence to warrant rejection of the managerʹs claim that production is not really out of control. 107) H0: p = H1: p > Test statistic: z = P-value: p = Critical value: z = Reject null hypothesis. There is sufficient evidence to warrant rejection of the claim that no more than 1% are defective. 108) H0: p = H1: p Test statistic: z = P-value: p = Critical value: z = ± Fail to reject null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the actual percentage is 53%. 109) A 110) C 111) A 112) H0: μ = 23; H1: μ > 23. Test statistic: z = ;. P-value: Because the P-value of is less than the significance level of α = 0.05, we reject the null hypothesis. 113) H0: μ = 200; H1: μ < 200; Test statistic: z = P-value: Fail to reject H0. There is not sufficient evidence to warrrant the rejection of the claim that the mean equals ) C 115) B 116) A 117) α = 0.1 Test statistic: t = 1.57 P-value: p = Because t < 1.729, we fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that μ = 132 lb. 118) α = 0.05 Test statistic: t = P-value: p = Because t < , we reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that μ = $30, ) α = 0.05 Test statistic: t = P-value: p = t > Because t > , we do not reject the null hypothesis. There is not sufficient evidence to support the claim that the mean age is less than 26 years. 120) Test statistic: t = Critical values: t = ± Reject H0: μ = There is sufficient evidence to support the claim that the mean is different from ) Test statistic: t = Critical values: t = , Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the mean is equal to ) Test statistic: t = Critical values: t = ± Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that the mean is 18.7 months. 123) B 124) C 125) D

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. STATISTICS/GRACEY PRACTICE TEST/EXAM 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the given random variable as being discrete or continuous.

More information

Chapter 7 - Practice Problems 1

Chapter 7 - Practice Problems 1 Chapter 7 - Practice Problems 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Define a point estimate. What is the

More information

Chapter 5 - Practice Problems 1

Chapter 5 - Practice Problems 1 Chapter 5 - Practice Problems 1 Identify the given random variable as being discrete or continuous. 1) The number of oil spills occurring off the Alaskan coast 1) A) Continuous B) Discrete 2) The ph level

More information

A) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777

A) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777 Math 210 - Exam 4 - Sample Exam 1) What is the p-value for testing H1: µ < 90 if the test statistic is t=-1.592 and n=8? A) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777 2) The owner of a football team claims that

More information

Chapter 7 - Practice Problems 2

Chapter 7 - Practice Problems 2 Chapter 7 - Practice Problems 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the requested value. 1) A researcher for a car insurance company

More information

Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions.

Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions. Chapter 4 & 5 practice set. The actual exam is not multiple choice nor does it contain like questions. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly

More information

1) The table lists the smoking habits of a group of college students. Answer: 0.218

1) The table lists the smoking habits of a group of college students. Answer: 0.218 FINAL EXAM REVIEW Name ) The table lists the smoking habits of a group of college students. Sex Non-smoker Regular Smoker Heavy Smoker Total Man 5 52 5 92 Woman 8 2 2 220 Total 22 2 If a student is chosen

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) ±1.88 B) ±1.645 C) ±1.96 D) ±2.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) ±1.88 B) ±1.645 C) ±1.96 D) ±2. Ch. 6 Confidence Intervals 6.1 Confidence Intervals for the Mean (Large Samples) 1 Find a Critical Value 1) Find the critical value zc that corresponds to a 94% confidence level. A) ±1.88 B) ±1.645 C)

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Ch. 4 Discrete Probability Distributions 4.1 Probability Distributions 1 Decide if a Random Variable is Discrete or Continuous 1) State whether the variable is discrete or continuous. The number of cups

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) 0.4987 B) 0.9987 C) 0.0010 D) 0.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) 0.4987 B) 0.9987 C) 0.0010 D) 0. Ch. 5 Normal Probability Distributions 5.1 Introduction to Normal Distributions and the Standard Normal Distribution 1 Find Areas Under the Standard Normal Curve 1) Find the area under the standard normal

More information

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing 1) Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures

More information

STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS

STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS 1. If two events (both with probability greater than 0) are mutually exclusive, then: A. They also must be independent. B. They also could

More information

Key Concept. Density Curve

Key Concept. Density Curve MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 6 Normal Probability Distributions 6 1 Review and Preview 6 2 The Standard Normal Distribution 6 3 Applications of Normal

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Regular smoker

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Regular smoker Exam Chapters 4&5 Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) A 28-year-old man pays $181 for a one-year

More information

5) The table below describes the smoking habits of a group of asthma sufferers. two way table ( ( cell cell ) (cell cell) (cell cell) )

5) The table below describes the smoking habits of a group of asthma sufferers. two way table ( ( cell cell ) (cell cell) (cell cell) ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine which score corresponds to the higher relative position. 1) Which score has a better relative

More information

Practice problems for Homework 12 - confidence intervals and hypothesis testing. Open the Homework Assignment 12 and solve the problems.

Practice problems for Homework 12 - confidence intervals and hypothesis testing. Open the Homework Assignment 12 and solve the problems. Practice problems for Homework 1 - confidence intervals and hypothesis testing. Read sections 10..3 and 10.3 of the text. Solve the practice problems below. Open the Homework Assignment 1 and solve the

More information

Chapter 4. Probability Distributions

Chapter 4. Probability Distributions Chapter 4 Probability Distributions Lesson 4-1/4-2 Random Variable Probability Distributions This chapter will deal the construction of probability distribution. By combining the methods of descriptive

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. STT315 Practice Ch 5-7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The length of time a traffic signal stays green (nicknamed

More information

BUS/ST 350 Exam 3 Spring 2012

BUS/ST 350 Exam 3 Spring 2012 BUS/ST 350 Exam 3 Spring 2012 Name Lab Section ID # INSTRUCTIONS: Write your name, lab section #, and ID# above. Note the statement at the bottom of this page that you must sign when you are finished with

More information

Module 2 Probability and Statistics

Module 2 Probability and Statistics Module 2 Probability and Statistics BASIC CONCEPTS Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The standard deviation of a standard normal distribution

More information

Unit 26 Estimation with Confidence Intervals

Unit 26 Estimation with Confidence Intervals Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference

More information

Mind on Statistics. Chapter 8

Mind on Statistics. Chapter 8 Mind on Statistics Chapter 8 Sections 8.1-8.2 Questions 1 to 4: For each situation, decide if the random variable described is a discrete random variable or a continuous random variable. 1. Random variable

More information

Find the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points. 2) 15% compounded semiannually

Find the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points. 2) 15% compounded semiannually Exam Name Find the compound amount for the deposit. Round to the nearest cent. 1) $1200 at 4% compounded quarterly for 5 years Find the effective rate corresponding to the given nominal rate. Round results

More information

AP STATISTICS (Warm-Up Exercises)

AP STATISTICS (Warm-Up Exercises) AP STATISTICS (Warm-Up Exercises) 1. Describe the distribution of ages in a city: 2. Graph a box plot on your calculator for the following test scores: {90, 80, 96, 54, 80, 95, 100, 75, 87, 62, 65, 85,

More information

Experimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test

Experimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test Experimental Design Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 To this point in the semester, we have largely

More information

STA 130 (Winter 2016): An Introduction to Statistical Reasoning and Data Science

STA 130 (Winter 2016): An Introduction to Statistical Reasoning and Data Science STA 130 (Winter 2016): An Introduction to Statistical Reasoning and Data Science Mondays 2:10 4:00 (GB 220) and Wednesdays 2:10 4:00 (various) Jeffrey Rosenthal Professor of Statistics, University of Toronto

More information

Example: Find the expected value of the random variable X. X 2 4 6 7 P(X) 0.3 0.2 0.1 0.4

Example: Find the expected value of the random variable X. X 2 4 6 7 P(X) 0.3 0.2 0.1 0.4 MATH 110 Test Three Outline of Test Material EXPECTED VALUE (8.5) Super easy ones (when the PDF is already given to you as a table and all you need to do is multiply down the columns and add across) Example:

More information

BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394

BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394 BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394 1. Does vigorous exercise affect concentration? In general, the time needed for people to complete

More information

MAT 155. Key Concept. September 27, 2010. 155S5.5_3 Poisson Probability Distributions. Chapter 5 Probability Distributions

MAT 155. Key Concept. September 27, 2010. 155S5.5_3 Poisson Probability Distributions. Chapter 5 Probability Distributions MAT 155 Dr. Claude Moore Cape Fear Community College Chapter 5 Probability Distributions 5 1 Review and Preview 5 2 Random Variables 5 3 Binomial Probability Distributions 5 4 Mean, Variance and Standard

More information

The Math. P (x) = 5! = 1 2 3 4 5 = 120.

The Math. P (x) = 5! = 1 2 3 4 5 = 120. The Math Suppose there are n experiments, and the probability that someone gets the right answer on any given experiment is p. So in the first example above, n = 5 and p = 0.2. Let X be the number of correct

More information

STT315 Chapter 4 Random Variables & Probability Distributions KM. Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables

STT315 Chapter 4 Random Variables & Probability Distributions KM. Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables Discrete vs. continuous random variables Examples of continuous distributions o Uniform o Exponential o Normal Recall: A random

More information

Chapter 7 Review. Confidence Intervals. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Chapter 7 Review. Confidence Intervals. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Chapter 7 Review Confidence Intervals MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Suppose that you wish to obtain a confidence interval for

More information

Ch5: Discrete Probability Distributions Section 5-1: Probability Distribution

Ch5: Discrete Probability Distributions Section 5-1: Probability Distribution Recall: Ch5: Discrete Probability Distributions Section 5-1: Probability Distribution A variable is a characteristic or attribute that can assume different values. o Various letters of the alphabet (e.g.

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Ch. 10 Chi SquareTests and the F-Distribution 10.1 Goodness of Fit 1 Find Expected Frequencies Provide an appropriate response. 1) The frequency distribution shows the ages for a sample of 100 employees.

More information

Probability Distributions

Probability Distributions Learning Objectives Probability Distributions Section 1: How Can We Summarize Possible Outcomes and Their Probabilities? 1. Random variable 2. Probability distributions for discrete random variables 3.

More information

Chapter 8 Section 1. Homework A

Chapter 8 Section 1. Homework A Chapter 8 Section 1 Homework A 8.7 Can we use the large-sample confidence interval? In each of the following circumstances state whether you would use the large-sample confidence interval. The variable

More information

Math 108 Exam 3 Solutions Spring 00

Math 108 Exam 3 Solutions Spring 00 Math 108 Exam 3 Solutions Spring 00 1. An ecologist studying acid rain takes measurements of the ph in 12 randomly selected Adirondack lakes. The results are as follows: 3.0 6.5 5.0 4.2 5.5 4.7 3.4 6.8

More information

3.4 Statistical inference for 2 populations based on two samples

3.4 Statistical inference for 2 populations based on two samples 3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted

More information

Joint Exam 1/P Sample Exam 1

Joint Exam 1/P Sample Exam 1 Joint Exam 1/P Sample Exam 1 Take this practice exam under strict exam conditions: Set a timer for 3 hours; Do not stop the timer for restroom breaks; Do not look at your notes. If you believe a question

More information

Chapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing

Chapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing 8-3 Testing a Claim About a Proportion 8-5 Testing a Claim About a Mean: s Not Known 8-6 Testing

More information

The Binomial Probability Distribution

The Binomial Probability Distribution The Binomial Probability Distribution MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2015 Objectives After this lesson we will be able to: determine whether a probability

More information

Hypothesis Testing. Steps for a hypothesis test:

Hypothesis Testing. Steps for a hypothesis test: Hypothesis Testing Steps for a hypothesis test: 1. State the claim H 0 and the alternative, H a 2. Choose a significance level or use the given one. 3. Draw the sampling distribution based on the assumption

More information

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as... HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

More information

Math 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2

Math 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2 Math 58. Rumbos Fall 2008 1 Solutions to Review Problems for Exam 2 1. For each of the following scenarios, determine whether the binomial distribution is the appropriate distribution for the random variable

More information

An Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10- TWO-SAMPLE TESTS

An Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10- TWO-SAMPLE TESTS The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10- TWO-SAMPLE TESTS Practice

More information

Math 251, Review Questions for Test 3 Rough Answers

Math 251, Review Questions for Test 3 Rough Answers Math 251, Review Questions for Test 3 Rough Answers 1. (Review of some terminology from Section 7.1) In a state with 459,341 voters, a poll of 2300 voters finds that 45 percent support the Republican candidate,

More information

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96 1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

More information

Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion

Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion Chapter 8: Hypothesis Testing for One Population Mean, Variance, and Proportion Learning Objectives Upon successful completion of Chapter 8, you will be able to: Understand terms. State the null and alternative

More information

BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420

BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420 BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420 1. Which of the following will increase the value of the power in a statistical test

More information

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as... HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

More information

4. Continuous Random Variables, the Pareto and Normal Distributions

4. Continuous Random Variables, the Pareto and Normal Distributions 4. Continuous Random Variables, the Pareto and Normal Distributions A continuous random variable X can take any value in a given range (e.g. height, weight, age). The distribution of a continuous random

More information

Dawson College - Fall 2004 Mathematics Department

Dawson College - Fall 2004 Mathematics Department Dawson College - Fall 2004 Mathematics Department Final Examination Statistics (201-257-DW) No. Score Out of 1 8 2 10 3 8 Date: Thursday, December 16, 2004 Time: 9:30 12:30 Instructors: Kourosh A. Zarabi

More information

Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation

Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation Parkland College A with Honors Projects Honors Program 2014 Calculating P-Values Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating P-Values" (2014). A with Honors Projects.

More information

STAT 350 Practice Final Exam Solution (Spring 2015)

STAT 350 Practice Final Exam Solution (Spring 2015) PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects

More information

Name: Date: Use the following to answer questions 3-4:

Name: Date: Use the following to answer questions 3-4: Name: Date: 1. Determine whether each of the following statements is true or false. A) The margin of error for a 95% confidence interval for the mean increases as the sample size increases. B) The margin

More information

5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives

5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives C H 8A P T E R Outline 8 1 Steps in Traditional Method 8 2 z Test for a Mean 8 3 t Test for a Mean 8 4 z Test for a Proportion 8 6 Confidence Intervals and Copyright 2013 The McGraw Hill Companies, Inc.

More information

STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4

STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 Make sure you have 8 pages. You will be provided with a table as well, as a separate

More information

Statistics 151 Practice Midterm 1 Mike Kowalski

Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Multiple Choice (50 minutes) Instructions: 1. This is a closed book exam. 2. You may use the STAT 151 formula sheets and

More information

A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING CHAPTER 5. A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING 5.1 Concepts When a number of animals or plots are exposed to a certain treatment, we usually estimate the effect of the treatment

More information

University of Chicago Graduate School of Business. Business 41000: Business Statistics Solution Key

University of Chicago Graduate School of Business. Business 41000: Business Statistics Solution Key Name: OUTLINE SOLUTIONS University of Chicago Graduate School of Business Business 41000: Business Statistics Solution Key Special Notes: 1. This is a closed-book exam. You may use an 8 11 piece of paper

More information

Stats Review Chapters 9-10

Stats Review Chapters 9-10 Stats Review Chapters 9-10 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test

More information

Mind on Statistics. Chapter 12

Mind on Statistics. Chapter 12 Mind on Statistics Chapter 12 Sections 12.1 Questions 1 to 6: For each statement, determine if the statement is a typical null hypothesis (H 0 ) or alternative hypothesis (H a ). 1. There is no difference

More information

Introduction to Hypothesis Testing

Introduction to Hypothesis Testing I. Terms, Concepts. Introduction to Hypothesis Testing A. In general, we do not know the true value of population parameters - they must be estimated. However, we do have hypotheses about what the true

More information

b. What is the probability of an event that is certain to occur? ANSWER: P(certain to occur) = 1.0

b. What is the probability of an event that is certain to occur? ANSWER: P(certain to occur) = 1.0 MTH 157 Sample Test 2 ANSWERS Student Row Seat M157ST2a Chapters 3 & 4 Dr. Claude S. Moore Score SHOW ALL NECESSARY WORK. Be Neat and Organized. Good Luck. 1. In a statistics class, 12 students own their

More information

Chapter 1: Exploring Data

Chapter 1: Exploring Data Chapter 1: Exploring Data Chapter 1 Review 1. As part of survey of college students a researcher is interested in the variable class standing. She records a 1 if the student is a freshman, a 2 if the student

More information

Tests of Hypotheses Using Statistics

Tests of Hypotheses Using Statistics Tests of Hypotheses Using Statistics Adam Massey and Steven J. Miller Mathematics Department Brown University Providence, RI 0292 Abstract We present the various methods of hypothesis testing that one

More information

Chapter 7 Notes - Inference for Single Samples. You know already for a large sample, you can invoke the CLT so:

Chapter 7 Notes - Inference for Single Samples. You know already for a large sample, you can invoke the CLT so: Chapter 7 Notes - Inference for Single Samples You know already for a large sample, you can invoke the CLT so: X N(µ, ). Also for a large sample, you can replace an unknown σ by s. You know how to do a

More information

MA 1125 Lecture 14 - Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values.

MA 1125 Lecture 14 - Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values. MA 5 Lecture 4 - Expected Values Friday, February 2, 24. Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the

More information

Review. March 21, 2011. 155S7.1 2_3 Estimating a Population Proportion. Chapter 7 Estimates and Sample Sizes. Test 2 (Chapters 4, 5, & 6) Results

Review. March 21, 2011. 155S7.1 2_3 Estimating a Population Proportion. Chapter 7 Estimates and Sample Sizes. Test 2 (Chapters 4, 5, & 6) Results MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 7 Estimates and Sample Sizes 7 1 Review and Preview 7 2 Estimating a Population Proportion 7 3 Estimating a Population

More information

6. Let X be a binomial random variable with distribution B(10, 0.6). What is the probability that X equals 8? A) (0.6) (0.4) B) 8! C) 45(0.6) (0.

6. Let X be a binomial random variable with distribution B(10, 0.6). What is the probability that X equals 8? A) (0.6) (0.4) B) 8! C) 45(0.6) (0. Name: Date:. For each of the following scenarios, determine the appropriate distribution for the random variable X. A) A fair die is rolled seven times. Let X = the number of times we see an even number.

More information

CHAPTER 6: Continuous Uniform Distribution: 6.1. Definition: The density function of the continuous random variable X on the interval [A, B] is.

CHAPTER 6: Continuous Uniform Distribution: 6.1. Definition: The density function of the continuous random variable X on the interval [A, B] is. Some Continuous Probability Distributions CHAPTER 6: Continuous Uniform Distribution: 6. Definition: The density function of the continuous random variable X on the interval [A, B] is B A A x B f(x; A,

More information

Opgaven Onderzoeksmethoden, Onderdeel Statistiek

Opgaven Onderzoeksmethoden, Onderdeel Statistiek Opgaven Onderzoeksmethoden, Onderdeel Statistiek 1. What is the measurement scale of the following variables? a Shoe size b Religion c Car brand d Score in a tennis game e Number of work hours per week

More information

Mind on Statistics. Chapter 15

Mind on Statistics. Chapter 15 Mind on Statistics Chapter 15 Section 15.1 1. A student survey was done to study the relationship between class standing (freshman, sophomore, junior, or senior) and major subject (English, Biology, French,

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 2. (b) 1.5. (c) 0.5-2.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 2. (b) 1.5. (c) 0.5-2. Stats: Test 1 Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given frequency distribution to find the (a) class width. (b) class

More information

Chapter 5: Normal Probability Distributions - Solutions

Chapter 5: Normal Probability Distributions - Solutions Chapter 5: Normal Probability Distributions - Solutions Note: All areas and z-scores are approximate. Your answers may vary slightly. 5.2 Normal Distributions: Finding Probabilities If you are given that

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Sample Practice problems - chapter 12-1 and 2 proportions for inference - Z Distributions Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide

More information

Statistics Class Level Test Mu Alpha Theta State 2008

Statistics Class Level Test Mu Alpha Theta State 2008 Statistics Class Level Test Mu Alpha Theta State 2008 1. Which of the following are true statements? I. The histogram of a binomial distribution with p = 0.5 is always symmetric no matter what n, the number

More information

Summary of Formulas and Concepts. Descriptive Statistics (Ch. 1-4)

Summary of Formulas and Concepts. Descriptive Statistics (Ch. 1-4) Summary of Formulas and Concepts Descriptive Statistics (Ch. 1-4) Definitions Population: The complete set of numerical information on a particular quantity in which an investigator is interested. We assume

More information

Practice Problems and Exams

Practice Problems and Exams Practice Problems and Exams 1 The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 1302) Spring Semester 2009-2010

More information

MATH 2200 PROBABILITY AND STATISTICS M2200FL083.1

MATH 2200 PROBABILITY AND STATISTICS M2200FL083.1 MATH 2200 PROBABILITY AND STATISTICS M2200FL083.1 In almost all problems, I have given the answers to four significant digits. If your answer is slightly different from one of mine, consider that to be

More information

Chapter 2. Hypothesis testing in one population

Chapter 2. Hypothesis testing in one population Chapter 2. Hypothesis testing in one population Contents Introduction, the null and alternative hypotheses Hypothesis testing process Type I and Type II errors, power Test statistic, level of significance

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data. 1) Frank's Furniture employees earned the following

More information

MATH 103/GRACEY PRACTICE EXAM/CHAPTERS 2-3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MATH 103/GRACEY PRACTICE EXAM/CHAPTERS 2-3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MATH 3/GRACEY PRACTICE EXAM/CHAPTERS 2-3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The frequency distribution

More information

Answers: a. 87.5325 to 92.4675 b. 87.06 to 92.94

Answers: a. 87.5325 to 92.4675 b. 87.06 to 92.94 1. The average monthly electric bill of a random sample of 256 residents of a city is $90 with a standard deviation of $24. a. Construct a 90% confidence interval for the mean monthly electric bills of

More information

Statistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013

Statistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013 Statistics I for QBIC Text Book: Biostatistics, 10 th edition, by Daniel & Cross Contents and Objectives Chapters 1 7 Revised: August 2013 Chapter 1: Nature of Statistics (sections 1.1-1.6) Objectives

More information

WISE Power Tutorial All Exercises

WISE Power Tutorial All Exercises ame Date Class WISE Power Tutorial All Exercises Power: The B.E.A.. Mnemonic Four interrelated features of power can be summarized using BEA B Beta Error (Power = 1 Beta Error): Beta error (or Type II

More information

AP Statistics 7!3! 6!

AP Statistics 7!3! 6! Lesson 6-4 Introduction to Binomial Distributions Factorials 3!= Definition: n! = n( n 1)( n 2)...(3)(2)(1), n 0 Note: 0! = 1 (by definition) Ex. #1 Evaluate: a) 5! b) 3!(4!) c) 7!3! 6! d) 22! 21! 20!

More information

Lecture Notes Module 1

Lecture Notes Module 1 Lecture Notes Module 1 Study Populations A study population is a clearly defined collection of people, animals, plants, or objects. In psychological research, a study population usually consists of a specific

More information

6.4 Normal Distribution

6.4 Normal Distribution Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under

More information

p ˆ (sample mean and sample

p ˆ (sample mean and sample Chapter 6: Confidence Intervals and Hypothesis Testing When analyzing data, we can t just accept the sample mean or sample proportion as the official mean or proportion. When we estimate the statistics

More information

Density Curve. A density curve is the graph of a continuous probability distribution. It must satisfy the following properties:

Density Curve. A density curve is the graph of a continuous probability distribution. It must satisfy the following properties: Density Curve A density curve is the graph of a continuous probability distribution. It must satisfy the following properties: 1. The total area under the curve must equal 1. 2. Every point on the curve

More information

Practice Midterm Exam #2

Practice Midterm Exam #2 The Islamic University of Gaza Faculty of Engineering Department of Civil Engineering 12/12/2009 Statistics and Probability for Engineering Applications 9.2 X is a binomial random variable, show that (

More information

In the general population of 0 to 4-year-olds, the annual incidence of asthma is 1.4%

In the general population of 0 to 4-year-olds, the annual incidence of asthma is 1.4% Hypothesis Testing for a Proportion Example: We are interested in the probability of developing asthma over a given one-year period for children 0 to 4 years of age whose mothers smoke in the home In the

More information

Introduction to Hypothesis Testing OPRE 6301

Introduction to Hypothesis Testing OPRE 6301 Introduction to Hypothesis Testing OPRE 6301 Motivation... The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about

More information

Section 6.1 Discrete Random variables Probability Distribution

Section 6.1 Discrete Random variables Probability Distribution Section 6.1 Discrete Random variables Probability Distribution Definitions a) Random variable is a variable whose values are determined by chance. b) Discrete Probability distribution consists of the values

More information

Probability Distributions

Probability Distributions CHAPTER 5 Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Probability Distribution 5.3 The Binomial Distribution

More information

Chapter 3 RANDOM VARIATE GENERATION

Chapter 3 RANDOM VARIATE GENERATION Chapter 3 RANDOM VARIATE GENERATION In order to do a Monte Carlo simulation either by hand or by computer, techniques must be developed for generating values of random variables having known distributions.

More information

Ch. 6.1 #7-49 odd. The area is found by looking up z= 0.75 in Table E and subtracting 0.5. Area = 0.7734-0.5= 0.2734

Ch. 6.1 #7-49 odd. The area is found by looking up z= 0.75 in Table E and subtracting 0.5. Area = 0.7734-0.5= 0.2734 Ch. 6.1 #7-49 odd The area is found by looking up z= 0.75 in Table E and subtracting 0.5. Area = 0.7734-0.5= 0.2734 The area is found by looking up z= 2.07 in Table E and subtracting from 0.5. Area = 0.5-0.0192

More information

Normal Probability Distribution

Normal Probability Distribution Normal Probability Distribution The Normal Distribution functions: #1: normalpdf pdf = Probability Density Function This function returns the probability of a single value of the random variable x. Use

More information