Review #2. Statistics

Review #2 Statistics Find the mean of the given probability distribution. 1) x P(x) 0 0.19 1 0.37 2 0.16 3 0.26 4 0.02 A) 1.64 B) 1.45 C) 1.55 D) 1.74 2) The number of golf balls ordered by customers of a pro shop has the following probability distribution. x 3 6 9 12 15 p(x) 0.14 0.11 0.36 0.29 0.10 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 0.5470, 0.3562, 0.0870, 0.0094, and 0.0004, respectively. Round answer to the nearest hundredth. A) 1.11 B) 0.56 C) 0.46 D) 2.00 4) 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) 0 0.17 1 0.28 2 0.05 3 0.15 4 0.35 A) 7.43 B) 2.63 C) 2.46 D) 2.69 6) Find the variance for the given probability distribution. x P(x) 0 0.05 2 0.17 4 0.43 6 0.35 A) 2.85 B) 2.44 C) 1.56 D) 1.69

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) 0 0.0256 1 0.1536 2 0.3456 3 0.3456 4 0.1296 A) 0.84 B) 0.98 C) 6.72 D) 0.96 8) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Find the variance for the probability distribution. A) 0.77 B) 0.59 C) 1.11 D) 0.51 9) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.6274, 0.3102, 0.0575, 0.0047, and 0.0001, respectively. Find the standard deviation for the probability distribution. A) 0.56 B) 0.76 C) 0.63 D) 0.39 10) 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) 0.98 11) 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) -$6.83 12) 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.

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) 0.0231 B) 0.0154 C) 0.0039 D) 0.0116 17) n = 6, x = 3, p = 1 6 A) 0.0536 B) 0.0286 C) 0.0154 D) 0.0322 18) n = 10, x = 2, p = 1 3 A) 0.1951 B) 0.2156 C) 0.0028 D) 0.1929 19) n = 5, x = 2, p = 0.70 A) 0.464 B) 0.700 C) 0.132 D) 0.198 20) n = 30, x = 12, p = 0.20 A) 0.1082 B) 0.0064 C) 0.0139 D) 0.0028 21) n =12, x = 5, p = 0.25 A) 0.082 B) 0.103 C) 0.091 D) 0.027 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) 0.172 B) 0.945 C) 0.117 D) 0.055 23) 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) 0.0547 B) 0.9815 C) 0.9846 D) 0.913 24) 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) 0.044 B) 0.945 C) 0.011 D) 0.989 25) 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) 0.2154 B) 0.3340 C) 0.8051 D) 0.5494 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 = 6.9 27) n = 20; p = 3/5 A) μ = 12.7 B) μ = 12.0 C) μ = 12.3 D) μ = 11.5

28) n = 665; p =.7 A) μ = 465.5 B) μ = 467.2 C) μ = 466.8 D) μ = 464.0 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 = -0.01 C) σ = 6.52 D) σ = 5.67 30) n = 25; p = 3/5 A) σ = 5.72 B) σ = 2.45 C) σ = 6.57 D) σ = 0.04 31) n = 574; p =.7 A) σ = 10.98 B) σ = 15.10 C) σ = 8.57 D) σ = 14.25 32) n = 2661; p =.63 A) σ = 29.03 B) σ = 28.18 C) σ = 22.50 D) σ = 24.91 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: -11.28; maximum: 48.88 B) Minimum: 11.04; maximum: 26.56 C) Minimum: 14.92; maximum: 22.68 D) Minimum: 26.56; maximum: 11.04 34) n = 189, p = 0.13 A) Minimum: -18.18; maximum: 67.32 B) Minimum: 33.82; maximum: 15.32 C) Minimum: 19.95; maximum: 29.19 D) Minimum: 15.32; maximum: 33.82 35) n = 1100, p = 0.84 A) Minimum: 911.84; maximum: 936.16 B) Minimum: 906.8; maximum: 941.2 C) Minimum: 899.68; maximum: 948.32 D) Minimum: 948.32; maximum: 899.68 36) n = 1104, p = 0.93 A) Minimum: 1014.73; maximum: 1038.71 B) Minimum: 1018.24; maximum: 1035.2 C) Minimum: 1009.76; maximum: 1043.68 D) Minimum: 1043.68; maximum: 1009.76 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) 2.75 38) 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) 1.75 39) 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

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) 0.750 B) 0.625 C) 0.575 D) 0.500 43) What is the probability that the random variable has a value greater than 5.3? A) 0.3375 B) 0.2875 C) 0.4625 D) 0.2125 44) What is the probability that the random variable has a value less than 6? A) 0.875 B) 0.625 C) 0.750 D) 0.500 If Z is a standard normal variable, find the probability. 45) The probability that Z lies between 0 and 3.01 A) 0.1217 B) 0.9987 C) 0.5013 D) 0.4987 46) The probability that Z lies between -2.41 and 0 A) 0.5080 B) 0.4920 C) 0.0948 D) 0.4910 47) The probability that Z is less than 1.13 A) 0.8485 B) 0.8708 C) 0.1292 D) 0.8907 48) The probability that Z lies between -1.10 and -0.36 A) 0.2239 B) -0.2237 C) 0.4951 D) 0.2237 49) The probability that Z lies between 0.7 and 1.98 A) 0.2181 B) 0.2175 C) 1.7341 D) -0.2181 50) The probability that Z lies between -0.55 and 0.55 A) -0.4176 B) -0.9000 C) 0.9000 D) 0.4176 51) The probability that Z is greater than -1.82 A) 0.9656 B) 0.0344 C) -0.0344 D) 0.4656

52) P(Z > 0.59) A) 0.7224 B) 0.2190 C) 0.2776 D) 0.2224 53) P(Z < 0.97) A) 0.1660 B) 0.8078 C) 0.8340 D) 0.8315 54) P(-0.73 < Z < 2.27) A) 0.4884 B) 0.7557 C) 1.54 D) 0.2211 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) -0.25 B) 0.25 C) -0.57 D) 0.57 56) Find Q3, the third quartile. A) -1.3 B) 0.82 C) 0.53 D) 0.67 57) 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 53.0. A) 0.5589 B) 0.0802 C) 0.9599 D) 0.0401 59) The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than 15.2. A) 0.5000 B) 1.0000 C) 0.9998 D) 0.0003 60) The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than 16.1. A) 0.1357 B) 0.8413 C) 0.1550 D) 0.1587 61) The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find the probability that X is between 14.3 and 16.1. A) 0.3413 B) 0.8413 C) 0.1587 D) 0.6826 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) 1078.3 B) 1021.7 C) 1087.8 D) 1148.1

63) Scores on a test are normally distributed with a mean of 65.3 and a standard deviation of 10.3. Find P81, which separates the bottom 81% from the top 19%. A) 0.88 B) 74.4 C) 68.3 D) 0.291 64) 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) 207.8 B) 187.5 C) 212.5 D) 211.3 65) 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) 0.2177 B) 0.7823 C) 0.2823 D) 0.1003 Find the margin of error for the 95% confidence interval used to estimate the population proportion. 69) n = 169, x = 107 A) 0.0727 B) 0.127 C) 0.0654 D) 0.00269 70) n = 230, x = 90 A) 0.0631 B) 0.0568 C) 0.0663 D) 0.0757 71) In a survey of 4100 T.V. viewers, 20% said they watch network news programs. A) 0.0140 B) 0.00915 C) 0.0160 D) 0.0122 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) 0.354 < p < 0.612 B) 0.375 < p < 0.591 C) 0.374 < p < 0.592 D) 0.353 < p < 0.613 73) n = 84, x = 37; 98 percent A) 0.314 < p < 0.566 B) 0.313 < p < 0.567 C) 0.334 < p < 0.546 D) 0.333 < p < 0.547 74) n = 102, x = 52; 88 percent A) 0.428 < p < 0.592 B) 0.433 < p < 0.587 C) 0.429 < p < 0.591 D) 0.432 < p < 0.588 75) n = 133, x = 82; 90 percent A) 0.550 < p < 0.684 B) 0.551 < p < 0.683 C) 0.548 < p < 0.686 D) 0.546 < p < 0.688

76) n = 182, x = 135; 95 percent A) 0.677 < p < 0.806 B) 0.691 < p < 0.792 C) 0.690 < p < 0.793 D) 0.678 < p < 0.805 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) 8218 78) 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) 177 79) 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) 0.444 < p < 0.500 B) 0.435 < p < 0.508 C) 0.438 < p < 0.505 D) 0.471 < p < 0.472 81) 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) 0.0118 < p < 0.0576 B) 0.0110 < p < 0.0584 C) 0.0345 < p < 0.0349 D) 0.0154 < p < 0.0540 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 < 80.8 86) 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 < 43.5 87) 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

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) 0.180 B) 0.200 C) 0.171 D) 0.212 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 < 16.31 B) 9.31 < μ < 16.29 C) 9.35 < μ < 16.25 D) 9.96 < μ < 15.64 95) n = 12, x = 19.1, s = 5.0, 99 percent A) 14.62 < μ < 23.58 B) 15.18 < μ < 23.02 C) 14.53 < μ < 23.67 D) 14.63 < μ < 23.57 96) n = 30, x = 86.5, s = 10.3, 90 percent A) 83.32 < μ < 89.68 B) 81.32 < μ < 91.68 C) 83.31 < μ < 89.69 D) 82.65 < μ < 90.35 97) The principal randomly selected six students to take an aptitude test. Their scores were: 77.9 89.1 80.7 78.6 74.4 82.0 Determine a 90 percent confidence interval for the mean score for all students. A) 84.64 < μ < 76.26 B) 84.54 < μ < 76.36 C) 76.36 < μ < 84.54 D) 76.26 < μ < 84.64 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) 34.805 B) 37.156 C) 7.015 D) 6.265

99) Find the critical value χ 2 L corresponding to a sample size of 9 and a confidence level of 90 percent. A) 2.733 B) 1.646 C) 20.09 D) 15.507 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 = 160.9 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 < 0.0011 B) H0: p = 0.0011 C) H0: p > 0.0011 D) H0: p = 0.0011 H1: p 0.0011 H1: p < 0.0011 H1: p 0.0011 H1: p > 0.0011 104) 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 > 30 105) 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 < 0.002 H1: p 0.002 B) H0: p = 0.002 H1: p < 0.002 C) H0: p = 0.002 H1: p > 0.002 D) H0: p > 0.002 H1: p 0.002 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.

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) 0.1539 B) 0.3461 C) 0.1635 D) 0.3078 110) 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) -0.2843 B) 0.2157 C) 0.5686 D) 0.2843 111) 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) 0.0048 B) 0.0024 C) 0.0262 D) 0.0524 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 183.9 lb. Assuming that σ is known to be 121.2 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 = 15.2. 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 = 15.3. 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 = 0.1. 118) 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.

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 = 0.05. 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 32.6. The sample data consists of 15 scores for which x = 39.7 and s = 5. 121) 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 35.0. 122) 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, 21.666 B) 1.735, 23.589 C) 21.666 D) 23.209 124) H1: σ > 3.5 n = 14 α = 0.05 A) 23.685 B) 24.736 C) 22.362 D) 5.892 125) H1: σ < 0.14 n = 23 α = 0.10 A) 30.813 B) -30.813 C) 14.848 D) 14.042

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

Answer Key Testname: REVIEW 2 103) B 104) D 105) B 106) H0: p = 0.03. H1: p > 0.03. Test statistic: z = 1.57. P-value: p = 0.0582. Critical value: z = 2.33. 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 = 0.01. H1: p > 0.01. Test statistic: z = 4.92. P-value: p = 0.0001. Critical value: z = 2.33. Reject null hypothesis. There is sufficient evidence to warrant rejection of the claim that no more than 1% are defective. 108) H0: p = 0.53. H1: p 0.53. Test statistic: z = -1.60. P-value: p = 0.0548. Critical value: z = ±1.645. 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 = -12.65;. P-value: 0.0001. Because the P-value of 0.0001 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 = -0.98. P-value: 0.1635. Fail to reject H0. There is not sufficient evidence to warrrant the rejection of the claim that the mean equals 200. 114) C 115) B 116) A 117) α = 0.1 Test statistic: t = 1.57 P-value: p = 0.1318 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 = -2.24 P-value: p = 0.0399 Because t < -2.120, we reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that μ = $30,000. 119) α = 0.05 Test statistic: t = -0.87 P-value: p = 0.1966 t > -1.711 Because t > -1.711, 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 = 5.50. Critical values: t = ±2.145. Reject H0: μ = 32.6. There is sufficient evidence to support the claim that the mean is different from 32.6. 121) Test statistic: t = 7.252. Critical values: t = -2.861, 2.861. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the mean is equal to 35.0. 122) Test statistic: t = 0.76. Critical values: t = ±2.228. 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