4) A researcher randomly selects and interviews fifty male and fifty female teachers. 4)

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1 THT # 4 STAT 2023 SPR'11 Due Wed. April 6 NO EXCEPTIONS Name SHOW ALL WORK ATTACHED Use the given data to construct a frequency distribution. 1) Kevin asked some of his friends how many hours they had worked during the previous week at their after-school jobs. The results are shown below Construct a frequency distribution. Use 4 classes, a class width of 2 hours, and a lower limit of 3 for class 1. Hours Frequency 1) Identify the sampling technique used. 2) At a local community college, five statistics classes are randomly selected out of 20 and all of the students from each class are interviewed. 2) 3) A community college student interviews everyone in a statistics class to determine the percentage of students that own a car. 3) 4) A researcher randomly selects and interviews fifty male and fifty female teachers. 4) 5) The names of 70 contestants are written on 70 cards. The cards are placed in a bag, and three names are picked from the bag. A) systematic B) random C) convenience D) stratified E) cluster 6) The table lists the smoking habits of a group of college students. 5) 6) Sex Non-smoker Regular Smoker Heavy Smoker Total Man Woman Total If a student is chosen at random, find the probability of getting someone who is a man or a woman. Round your answer to three decimal places. A) 1 B) C) D) ) If one card is drawn from a standard 52 card playing deck, determine the probability of getting a seven or a nine or a heart or a diamond. A) 0.50 B) 0.57 C) 0.65 D) ) 1

2 8) A test consists of 60 multiple choice questions, each with five possible answers, only one of which is correct. Find the mean and the standard deviation of the number of correct answers. A) mean: 30; standard deviation: B) mean: 12; standard deviation: C) mean: 12; standard deviation: D) mean: 30; standard deviation: ) A test consists of 690 true or false questions. If the student guesses on each question, what is the mean number of correct answers? A) 690 B) 0 C) 138 D) ) The probability that a house in an urban area will be burglarized is 2%. If 29 houses are randomly selected, what is the probability that none of the houses will be burglarized? A) B) C) D) ) Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly six boys in ten births. A) B) 0.6 C) 0.06 D) ) Investing is a game of chance. Suppose there is a 34% chance that a risky stock investment will end up in a total loss of your investment. Because the rewards are so high, you decide to invest in three independent risky stocks. Find the probability that at least one of your three investments becomes a total loss. A) B) C) D) ) One hundred people were asked, "Do you favor the death penalty?" Of the 33 that answered "yes" to the question, 14 were male. Of the 67 that answered "no" to the question, six were male. If one person is selected at random, what is the probability that this person answered "yes" or was a male? A) 0.39 B) 0.13 C) 0.67 D) ) 9) 10) 11) 12) 13) Find the number of standard deviations from the mean. Round your answer to two decimal places. 14) Mario's weekly poker winnings have a mean of $344 and a standard deviation of $51. Last week he won $178. How many standard deviations from the mean is that? A) 3.25 standard deviations above the mean B) 3.25 standard deviations below the mean C) 1.63 standard deviations above the mean D) 1.63 standard deviations below the mean 14) Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual. Consider a score to be unusual if its z-score is less than or greater than Round the z-score to the nearest tenth if necessary. 15) A body temperature of 99.5 F given that human body temperatures have a mean of F and a 15) standard deviation of A) 2.1; not unusual B) 2.1; unusual C) -2.1; unusual D) 1.3; not usual 16) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is less than 70. A) B) C) D) ) 2

3 Find the indicated measure. 17) The weights (in pounds) of 30 newborn babies are listed below. Find P A) 6.0 lb B) 6.1 lb C) 5.9 lb D) 4.8 lb 17) Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. 18) With n = 20 and p = 0.60, estimate P(fewer than 8). 18) A) B) C) D) ) A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses, estimate the probability of getting at least 20% correct. A) B) C) D) ) 20) The standard error of the mean is given by 20) A) µ ± B) C) µ - x D) µ - x n 21) Suppose a population has a mean of 7 for some characteristic of interest and a standard deviation of 9.6. A sample is drawn from this population of size 64. What is the standard error of the mean? A) 1.2 B) 0.15 C) 0.7 D) ) Assume that the heights of men are normally distributed with a mean of 70.1 inches and a standard deviation of 2.8 inches. If 64 men are randomly selected, find the probability that they have a mean height greater than 71.1 inches. A) B) C) D) ) 22) 23) Find the area under the standard normal curve between z = 1.5 and z = ) A) B) C) D) ) Find the sum of the areas under the standard normal curve to the left of z = and to the right of z = A) B) C) D) ) Given a distribution that follows a standard normal curve, what does the graph of the curve do as z increases in the positive direction? A) The graph of the curve eventually intersects the horizontal axis. B) The graph of the curve approaches an inflection point. C) The graph of the curve approaches 1. D) The graph of the curve approaches zero. 24) 25) 26) For a standard normal curve, find the z-score that separates the bottom 90% from the top 10%. 26) A) 2.81 B) 1.28 C) 1.52 D) 0.28 Find the indicated critical z value. 27) Find the critical value z /2 that corresponds to a 91% confidence level. 27) A) 1.70 B) 1.34 C) D)

4 28) Find the critical value z /2 that corresponds to a 94% confidence level. 28) A) B) 1.96 C) 1.88 D) 2.75 Express the confidence interval using the indicated format. 29) Express the confidence interval < p < in the form of p ± E. 29) A) ± 0.23 B) C) 0.23 ± 0.5 D) ± ) Express the confidence interval 0.66 < p < 0.8 in the form of p ± E. 30) A) 0.73 ± 0.07 B) 0.66 ± 0.14 C) 0.66 ± 0.07 D) 0.73 ± ) The following confidence interval is obtained for a population proportion, p: (0.505, 0.545). Use these confidence interval limits to find the point estimate, p. A) B) C) D) ) The following confidence interval is obtained for a population proportion, p: < p < Use these confidence interval limits to find the point estimate, p. A) B) C) D) ) 32) Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 33) 95% confidence; n = 320, x = 60 33) A) B) C) D) ) 90% confidence; n = 480, x = ) A) B) C) D) ) In a clinical test with 3300 subjects, 660 showed improvement from the treatment. Find the margin of error for the 99% confidence interval used to estimate the population proportion. A) B) C) D) ) Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 36) n = 51, x = 27; 95% confidence 36) A) < p < B) < p < C) < p < D) < p < Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 37) 99% confidence; n = 6500, x = ) A) B) C) D) Use the given data to find the minimum sample size required to estimate the population proportion. 38) Margin of error: 0.004; confidence level: 95%; p and q unknown 38) A) 60,148 B) 50,024 C) 60,018 D) 60,025 4

5 39) The following confidence interval is obtained for a population proportion, p: < p < Use these confidence interval limits to find the margin of error, E. A) B) C) D) ) Use the given data to find the minimum sample size required to estimate the population proportion. 40) Margin of error: 0.015; confidence level: 96%; p and q unknown 40) A) 4519 B) 4670 C) 6669 D) ) Margin of error: 0.05; confidence level: 99%; from a prior study, p is estimated by ) A) 407 B) 17 C) 339 D) 196 Round the point estimate to the nearest thousandth. 42) 50 people are selected randomly from a certain population and it is found that 13 people in the sample are over 6 feet tall. What is the point estimate of the proportion of people in the population who are over 6 feet tall? A) 0.26 B) 0.50 C) 0.19 D) ) Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. 43) Of 234 employees selected randomly from one company, 12.82% of them commute by carpooling. 43) Construct a 90% confidence interval for the true percentage of all employees of the company who carpool. A) 7.73% < p < 17.9% B) 8.54% < p < 17.1% C) 9.23% < p < 16.4% D) 7.18% < p < 18.5% 44) 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 140 adults selected randomly from one town, 35 of them smoke. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke. A) 16.5% < p < 33.5% B) 17.8% < p < 32.2% C) 19.0% < p < 31.0% D) 15.6% < p < 34.4% 44) 45) 46) In a certain population, body weights are normally distributed with a mean of 152 pounds and a standard deviation of 26 pounds. How many people must be surveyed if we want to estimate the percentage who weigh more than 180 pounds? Assume that we want 96% confidence that the error is no more than 4 percentage points. 46) 47) A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99 cases out of 100 should differ by no more than 5 percentage points in either direction from what would have been obtained by interviewing all voters in the United States." Find the sample size suggested by this statement. 47) 5

6 Find the indicated critical z value. 48) Find the critical value z /2 that corresponds to a 98% confidence level. 48) A) B) 2.05 C) 1.75 D) 2.33 Determine whether the given conditions justify using the margin of error E = z /2 / n when finding a confidence interval estimate of the population mean µ. 49) The sample size is n = 4, = 12.7, and the original population is normally distributed. 49) A) No B) Yes 50) The sample size is n = 200 and = ) A) Yes B) No Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted. 51) Replacement times for washing machines: 90% confidence; n = 45, x = 11.9 years, = 2.0 years 51) A) 2.9 yr B) 0.5 yr C) 0.4 yr D) 0.1 yr 52) The duration of telephone calls directed by a local telephone company: = 3.6 minutes, n = 560, 90% confidence. Round your answer to the nearest thousandth. A) min B) min C) min D) min 52) Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your answer to the same number of decimal places as the sample mean. 53) 37 packages are randomly selected from packages received by a parcel service. The sample 53) has a mean weight of 17.0 pounds and a standard deviation of 3.3 pounds. What is the 95% confidence interval for the true mean weight, µ, of all packages received by the parcel service? Use the given information to find the minimum sample size required to estimate an unknown population mean µ. 54) Margin of error: $120, confidence level: 95%, = $593 54) 55) How many weeks of data must be randomly sampled to estimate the mean weekly sales of a new line of athletic footwear? We want 99% confidence that the sample mean is within $200 of the population mean, and the population standard deviation is known to be $ ) 56) A 99% confidence interval (in inches) for the mean height of a population is < µ < This result is based on a sample of size 144. If the confidence interval < µ < is obtained from the same sample data, what is the degree of confidence? (Hint: you will first need to find the sample mean and sample standard deviation). A) 93% B) 92% C) 95% D) 94% 56) Do one of the following, as appropriate: (a) Find the critical value z /2, (b) find the critical value t /2, (c) state that neither the normal nor the t distribution applies. 57) 98%; n = 7; = 27; population appears to be normally distributed. 57) A) z /2 = 2.33 B) t /2 = 1.96 C) t /2 = D) z /2 = ) 91%; n = 45; is known; population appears to be very skewed. 58) A) t /2 = 1.34 B) z /2 = 1.70 C) z /2 = 1.75 D) t /2 =

7 59) How much money does the average professional football fan spend on food at a single football game? That question was posed to 10 randomly selected football fans. The sampled results show that sample mean and standard deviation were $18.00 and $3.30, respectively. Use this information to create a 95% confidence interval for the mean. A) 18 ± 2.228(3.30/ 10) B) 18 ± 2.262(3.30/ 10) C) 18 ± 1.833(3.30/ 10) D) 18 ± 2.201(3.30/ 10) 59) Do one of the following, as appropriate: (a) Find the critical value z /2, (b) find the critical value t /2, (c) state that neither the normal nor the t distribution applies. 60) 95%; n = 11; is known; population appears to be very skewed. 60) A) z /2 = 1.96 B) z /2 = C) t /2 = D) Neither the normal nor the t distribution applies. 61) 90%; n =9; = 4.2; population appears to be very skewed. 61) A) z /2 = B) Neither the normal nor the t distribution applies. C) z /2 = D) z /2 = ) Which of the following is not a characteristic of Students' t distribution? 62) A) depends on degrees of freedom. B) For large samples, the t and z distributions are nearly equivalent. C) symmetric distribution D) mean of 1 63) Find the critical t-value that corresponds to c = 0.95 and n = ) A) B) C) D) ) Find the critical t-value that corresponds to c = 0.90 and n = ) A) B) C) D) Assume that a sample is used to estimate a population mean µ. Use the given confidence level and sample data to find the margin of error. Assume that the sample is a simple random sample and the population has a normal distribution. Round your answer to one more decimal place than the sample standard deviation. _ 65) 95% confidence; n = 91; x = 16, s = ) A) 1.63 B) 4.10 C) 1.90 D) 1.71 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. 66) n = 10, x = 8.7, s = 3.3, 95% confidence 66) A) 6.79 < µ < B) 6.37 < µ < C) 6.35 < µ < D) 6.34 < µ < ) Thirty randomly selected students took the calculus final. If the sample mean was 83 and the standard deviation was 13.5, construct a 99% confidence interval for the mean score of all students. 67) 7

8 68) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 225 milligrams with s = 15.7 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs. 68) 69) The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were: Determine a 95% confidence interval for the mean time for all players. A) min < µ < 8.05 min B) 8.15 min < µ < min C) 8.05 min < µ < min D) min < µ < 8.15 min 69) 70) A researcher wishes to construct a 95% confidence interval for a population mean. She selects a simple random sample of size n = 20 from the population. The population is normally distributed and is known. When constructing the confidence interval, the researcher should use the normal distribution; however, she incorrectly uses the t distribution. How does this incorrectly calculated confidence relate to the correct confidence interval? A) The calculated confidence interval is wider than the correct confidence interval. B) The calculated confidence interval is narrower than the correct confidence interval. C) The calculated confidence interval is shifted to the right of the correct confidence interval. D) The calculated confidence interval is shifted to the left of the correct confidence interval. 71) A random sample of 10 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normally distributed. 70) 71) $3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00 Find the 95% confidence interval for the true mean. A) ($1.35, $2.85) B) ($4.81, $6.31) C) ($3.39, $6.01) D) ($2.11, $5.34) 72) To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette gave a mean nicotine content of 26.7 milligrams and standard deviation of 2.2 milligrams for a sample of n = 9 cigarettes. The FDA claims that the mean nicotine content exceeds 30.2 milligrams for this brand of cigarette, and their stated reliability is 99%. Do you agree? A) Yes, since the value 30.2 does fall in the 99% confidence interval. B) No, since the value 30.2 does fall in the 99% confidence interval. C) No, since the value 30.2 does not fall in the 99% confidence interval. D) Yes, since the value 30.2 does not fall in the 99% confidence interval. 72) 8

9 Construct a 95% Z-interval or a 95% t-interval about the population mean. Assume the data come from a population that is approximately normal with no outliers. 73) The heights of 20- to 29-year-old females are known to have a population standard deviation 73) = 2.7 inches. A simple random sample of n = 15 females 20 to 29 years old results in the following data: A) (64.85, 67.85); we are 95% confident that the mean height of 20- to 29-year-old females is between and inches. B) (65.20, 67.50); we are 95% confident that the mean height of 20- to 29-year-old females is between and inches. C) (65.12, 67.58); we are 95% confident that the mean height of 20- to 29-year-old females is between and inches. D) (64.98, 67.72); we are 95% confident that the mean height of 20- to 29-year-old females is between and inches. 74) Fifteen randomly selected men were asked to run on a treadmill for 6 minutes. After the 6 minutes, their pulses were measured and the following data were obtained: 74) A) (93.7, 107.1); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 93.7 and beats per minute. B) (95.2, 105.6); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 95.2 and beats per minute. C) (94.2, 106.6); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 94.2 and beats per minute. D) (94.9, 105.9); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 94.9 and beats per minute. 9