THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1306/STAT1603 Introductory Statistics (2015-2016) Assignment 5 Hand in Questions 4, 5, 8 and 9 on or before November 30, 2015 1. A plaque beside an elevator reads \"Capacity: 950 pounds, 6 persons\". Assume the weights of people entering the elevator are independently and identically distributed with = 150 pounds and standard deviation = 30 pounds. (a) A person is carrying a suitcase that weighs exactly ve times his own weight. What is the probability that the weight limit is exceeded? (b) If there are six people in the elevator, what is the probability that the weight limit is exceeded? (c) Repeat (b) if seven people crowd in. (d) What would be the answer to (c) if you are one of the seven and your weight is 135 pounds? 2. A paint manufacturer wants to determine the average drying time of a new interior wall paint. In 12 test areas of equal size, he obtained a mean drying time of 66.3 minutes and a standard deviation of 8.4 minutes. Construct a 95% condence interval for the true mean drying time. What assumption is needed in order to carry out the appropriate estimation procedure? 3. A random sample of 6 students in a physical education class had their pulse rates (beats per minute) measured before and after the 50-yard dash, with the following results: Student 1 2 3 4 5 6 Before 74 87 74 96 95 82 After 83 96 97 110 122 96 Construct a 95% condence interval for the mean increase in pulse rate. Also construct a 90% condence interval for the population standard deviation for the increase in pulse rate. 4. A process producing bricks is known to give an output whose weights are normally distributed with population standard deviation 0.12 kg. A random sample of sixteen bricks from today's output had a mean weight of 4.07 kg. (a) Find a 99% condence interval for the mean weight of all bricks produced this day. (b) It is decided that a sample of twenty bricks will be taken tomorrow. Without doing the calculations, state whether a 99% condence interval for the mean weight of tomorrow's output would be wider than, narrower than or the same width as that found in (a). (c) How many more bricks should be sampled so that the sample mean will be within 0.01 kg of the population mean with a probability of at least 0.99? 5. A study is being made to estimate the proportion of voters in a sizeable community who favor the construction of a nuclear power plant. If it is found that only 140 of 400 voters selected at random favor the project, nd a 95% condence interval for the proportion of all voters in this community who favor the project. STAT1306/1603: Assignment 5 2 6. To determine which of the two types of seeds was better, a state agricultural station chose 9 two-acre plots of land randomly within the state. Each plot was split in half, and a coin was tossed to determine in an unbiased way which half would be sown with seed A, and which half with seed B. The yields, in bushels, were recorded as follows: County P Q R S T U V H K Seed A 82 68 154 93 78 148 89 74 98 Seed B 89 69 173 91 81 150 97 64 117 Which seed is better? To back up your answer, construct an appropriate 95% condence interval and state the assumptions required. 7. An industrial psychologist wishes to study the eects of motivation on sales in a particular rm. Of 24 new salespersons, 12 are paid an hourly rate (Group A) and 12 are paid a commission (Group B). The 24 individuals are randomly assigned to the two groups. The following data represent the sales volume (in thousands of dollars) achieved during the rst month on the job. Hourly Rate 256 239 222 207 228 241 212 216 236 219 225 230 Commission 224 254 273 285 237 277 261 228 234 225 232 245 Assuming that the data come from independent normal populations with equal variance. Construct a 90% condence interval for the dierence of the two population means. Is there evidence that wage incentives through commission yield greater average sales volume? 8. High blood pressure (hypertension) is a leading cause of strokes. Medical researchers are constantly seeking ways to treat patients suering from this condition. A specialist in hypertension claims that regular aerobic exercise can reduce high blood pressure just as successfully as drugs, with none of the adverse side eects. To test this claim, 30 patients who suer from hypertension were chosen to participate in an experiment. For 60 days, 16 patients exercised three time per week for one hour (Group 1); and the other 14 patients took the standard medication (Group 2). The percentage reduction in blood pressure was recorded for each individual, and the following summary statistics were obtained: x1 = 13.2; x2 = 9.51; s1 = 2.68; s2 = 3.61. Construct a 95% condence interval for the dierence of the population mean percentage reduction in blood pressure between the two treatment groups. 9. Telemarketers obtain names and telephone numbers from several sources. To determine whether one particular source is better than a second, random samples of 400 and 420 names and numbers were obtained from sources A and B, respectively of which 52 and 46 from A and B made a purchase. Construct a 99% condence interval for pA pB , the dierence in the proportions of customers making a purchase from the two sources. THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1306/STAT1603 Introductory Statistics (2015-2016) Assignment 5 Hand in Questions 4, 5, 8 and 9 on or before November 30, 2015 1. A plaque beside an elevator reads \"Capacity: 950 pounds, 6 persons\". Assume the weights of people entering the elevator are independently and identically distributed with = 150 pounds and standard deviation = 30 pounds. (a) A person is carrying a suitcase that weighs exactly ve times his own weight. What is the probability that the weight limit is exceeded? (b) If there are six people in the elevator, what is the probability that the weight limit is exceeded? (c) Repeat (b) if seven people crowd in. (d) What would be the answer to (c) if you are one of the seven and your weight is 135 pounds? 2. A paint manufacturer wants to determine the average drying time of a new interior wall paint. In 12 test areas of equal size, he obtained a mean drying time of 66.3 minutes and a standard deviation of 8.4 minutes. Construct a 95% condence interval for the true mean drying time. What assumption is needed in order to carry out the appropriate estimation procedure? 3. A random sample of 6 students in a physical education class had their pulse rates (beats per minute) measured before and after the 50-yard dash, with the following results: Student 1 2 3 4 5 6 Before 74 87 74 96 95 82 After 83 96 97 110 122 96 Construct a 95% condence interval for the mean increase in pulse rate. Also construct a 90% condence interval for the population standard deviation for the increase in pulse rate. 4. A process producing bricks is known to give an output whose weights are normally distributed with population standard deviation 0.12 kg. A random sample of sixteen bricks from today's output had a mean weight of 4.07 kg. (a) Find a 99% condence interval for the mean weight of all bricks produced this day. (b) It is decided that a sample of twenty bricks will be taken tomorrow. Without doing the calculations, state whether a 99% condence interval for the mean weight of tomorrow's output would be wider than, narrower than or the same width as that found in (a). (c) How many more bricks should be sampled so that the sample mean will be within 0.01 kg of the population mean with a probability of at least 0.99? 5. A study is being made to estimate the proportion of voters in a sizeable community who favor the construction of a nuclear power plant. If it is found that only 140 of 400 voters selected at random favor the project, nd a 95% condence interval for the proportion of all voters in this community who favor the project. STAT1306/1603: Assignment 5 2 6. To determine which of the two types of seeds was better, a state agricultural station chose 9 two-acre plots of land randomly within the state. Each plot was split in half, and a coin was tossed to determine in an unbiased way which half would be sown with seed A, and which half with seed B. The yields, in bushels, were recorded as follows: County P Q R S T U V H K Seed A 82 68 154 93 78 148 89 74 98 Seed B 89 69 173 91 81 150 97 64 117 Which seed is better? To back up your answer, construct an appropriate 95% condence interval and state the assumptions required. 7. An industrial psychologist wishes to study the eects of motivation on sales in a particular rm. Of 24 new salespersons, 12 are paid an hourly rate (Group A) and 12 are paid a commission (Group B). The 24 individuals are randomly assigned to the two groups. The following data represent the sales volume (in thousands of dollars) achieved during the rst month on the job. Hourly Rate 256 239 222 207 228 241 212 216 236 219 225 230 Commission 224 254 273 285 237 277 261 228 234 225 232 245 Assuming that the data come from independent normal populations with equal variance. Construct a 90% condence interval for the dierence of the two population means. Is there evidence that wage incentives through commission yield greater average sales volume? 8. High blood pressure (hypertension) is a leading cause of strokes. Medical researchers are constantly seeking ways to treat patients suering from this condition. A specialist in hypertension claims that regular aerobic exercise can reduce high blood pressure just as successfully as drugs, with none of the adverse side eects. To test this claim, 30 patients who suer from hypertension were chosen to participate in an experiment. For 60 days, 16 patients exercised three time per week for one hour (Group 1); and the other 14 patients took the standard medication (Group 2). The percentage reduction in blood pressure was recorded for each individual, and the following summary statistics were obtained: x1 = 13.2; x2 = 9.51; s1 = 2.68; s2 = 3.61. Construct a 95% condence interval for the dierence of the population mean percentage reduction in blood pressure between the two treatment groups. 9. Telemarketers obtain names and telephone numbers from several sources. To determine whether one particular source is better than a second, random samples of 400 and 420 names and numbers were obtained from sources A and B, respectively of which 52 and 46 from A and B made a purchase. Construct a 99% condence interval for pA pB , the dierence in the proportions of customers making a purchase from the two sources. THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1306/STAT1603 Introductory Statistics (2015-2016) Assignment 5 Hand in Questions 4, 5, 8 and 9 on or before November 30, 2015 1. A plaque beside an elevator reads \"Capacity: 950 pounds, 6 persons\". Assume the weights of people entering the elevator are independently and identically distributed with = 150 pounds and standard deviation = 30 pounds. (a) A person is carrying a suitcase that weighs exactly ve times his own weight. What is the probability that the weight limit is exceeded? (b) If there are six people in the elevator, what is the probability that the weight limit is exceeded? (c) Repeat (b) if seven people crowd in. (d) What would be the answer to (c) if you are one of the seven and your weight is 135 pounds? 2. A paint manufacturer wants to determine the average drying time of a new interior wall paint. In 12 test areas of equal size, he obtained a mean drying time of 66.3 minutes and a standard deviation of 8.4 minutes. Construct a 95% condence interval for the true mean drying time. What assumption is needed in order to carry out the appropriate estimation procedure? 3. A random sample of 6 students in a physical education class had their pulse rates (beats per minute) measured before and after the 50-yard dash, with the following results: Student 1 2 3 4 5 6 Before 74 87 74 96 95 82 After 83 96 97 110 122 96 Construct a 95% condence interval for the mean increase in pulse rate. Also construct a 90% condence interval for the population standard deviation for the increase in pulse rate. 4. A process producing bricks is known to give an output whose weights are normally distributed with population standard deviation 0.12 kg. A random sample of sixteen bricks from today's output had a mean weight of 4.07 kg. (a) Find a 99% condence interval for the mean weight of all bricks produced this day. (b) It is decided that a sample of twenty bricks will be taken tomorrow. Without doing the calculations, state whether a 99% condence interval for the mean weight of tomorrow's output would be wider than, narrower than or the same width as that found in (a). (c) How many more bricks should be sampled so that the sample mean will be within 0.01 kg of the population mean with a probability of at least 0.99? 5. A study is being made to estimate the proportion of voters in a sizeable community who favor the construction of a nuclear power plant. If it is found that only 140 of 400 voters selected at random favor the project, nd a 95% condence interval for the proportion of all voters in this community who favor the project. STAT1306/1603: Assignment 5 2 6. To determine which of the two types of seeds was better, a state agricultural station chose 9 two-acre plots of land randomly within the state. Each plot was split in half, and a coin was tossed to determine in an unbiased way which half would be sown with seed A, and which half with seed B. The yields, in bushels, were recorded as follows: County P Q R S T U V H K Seed A 82 68 154 93 78 148 89 74 98 Seed B 89 69 173 91 81 150 97 64 117 Which seed is better? To back up your answer, construct an appropriate 95% condence interval and state the assumptions required. 7. An industrial psychologist wishes to study the eects of motivation on sales in a particular rm. Of 24 new salespersons, 12 are paid an hourly rate (Group A) and 12 are paid a commission (Group B). The 24 individuals are randomly assigned to the two groups. The following data represent the sales volume (in thousands of dollars) achieved during the rst month on the job. Hourly Rate 256 239 222 207 228 241 212 216 236 219 225 230 Commission 224 254 273 285 237 277 261 228 234 225 232 245 Assuming that the data come from independent normal populations with equal variance. Construct a 90% condence interval for the dierence of the two population means. Is there evidence that wage incentives through commission yield greater average sales volume? 8. High blood pressure (hypertension) is a leading cause of strokes. Medical researchers are constantly seeking ways to treat patients suering from this condition. A specialist in hypertension claims that regular aerobic exercise can reduce high blood pressure just as successfully as drugs, with none of the adverse side eects. To test this claim, 30 patients who suer from hypertension were chosen to participate in an experiment. For 60 days, 16 patients exercised three time per week for one hour (Group 1); and the other 14 patients took the standard medication (Group 2). The percentage reduction in blood pressure was recorded for each individual, and the following summary statistics were obtained: x1 = 13.2; x2 = 9.51; s1 = 2.68; s2 = 3.61. Construct a 95% condence interval for the dierence of the population mean percentage reduction in blood pressure between the two treatment groups. 9. Telemarketers obtain names and telephone numbers from several sources. To determine whether one particular source is better than a second, random samples of 400 and 420 names and numbers were obtained from sources A and B, respectively of which 52 and 46 from A and B made a purchase. Construct a 99% condence interval for pA pB , the dierence in the proportions of customers making a purchase from the two sources. THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1306/STAT1603 Introductory Statistics (2015-2016) Assignment 5 Hand in Questions 4, 5, 8 and 9 on or before November 30, 2015 A plaque beside an elevator reads \"Capacity: 950 pounds, 6 persons\". Assume the weights of people entering the elevator are independently and identically distributed with = 150 pounds and standard deviation = 30 pounds. A person is carrying a suitcase that weighs exactly five times his own weight. What is the probability that the weight limit is exceeded? If there are six people in the elevator, what is the probability that the weight limit is exceeded? Repeat (b) if seven people crowd in. What would be the answer to (c) if you are one of the seven and your weight is 135 pounds? A paint manufacturer wants to determine the average drying time of a new interior wall paint. In 12 test areas of equal size, he obtained a mean drying time of 66.3 minutes and a standard deviation of 8.4 minutes. Construct a 95% confidence interval for the true mean drying time. What assumption is needed in order to carry out the appropriate estimation procedure? A random sample of 6 students in a physical education class had their pulse rates (beats per minute) measured before and after the 50-yard dash, with the following results: Student 1 2 3 4 5 6 Before 74 87 74 96 95 82 After 83 96 97 110 122 96 Construct a 95% confidence interval for the mean increase in pulse rate. Also construct a 90% confidence interval for the population standard deviation for the increase in pulse rate. A process producing bricks is known to give an output whose weights are normally distributed with population standard deviation 0.12 kg. A random sample of sixteen bricks from today's output had a mean weight of 4.07 kg. Find a 99% confidence interval for the mean weight of all bricks produced this day. It is decided that a sample of twenty bricks will be taken tomorrow. Without doing the calculations, state whether a 99% confidence interval for the mean weight of tomorrow's output would be wider than, narrower than or the same width as that found in (a). How many more bricks should be sampled so that the sample mean will be within 0.01 kg of the population mean with a probability of at least 0.99? A study is being made to estimate the proportion of voters in a sizeable community who favor the construction of a nuclear power plant. If it is found that only 140 of 400 voters selected at random favor the project, find a 95% confidence interval for the proportion of all voters in this community who favor the project. STAT1306/1603: Assignment 5 2 To determine which of the two types of seeds was better, a state agricultural station chose 9 two-acre plots of land randomly within the state. Each plot was split in half, and a coin was tossed to determine in an unbiased way which half would be sown with seed A, and which half with seed B. The yields, in bushels, were recorded as follows: County P Q R S T U V H K Seed A 82 68 154 93 78 148 89 74 98 Seed B 89 69 173 91 81 150 97 64 117 Which seed is better? To back up your answer, construct an appropriate 95% confidence interval and state the assumptions required. 7. An industrial psychologist wishes to study the eects of motivation on sales in a particular firm. Of 24 new salespersons, 12 are paid an hourly rate (Group A) and 12 are paid a commission (Group B). The 24 individuals are randomly assigned to the two groups. The following data represent the sales volume (in thousands of dollars) achieved during the first month on the job. Hourly Rate 256 239 222 207 228 241 212 216 236 219 225 230 Commission 224 254 273 285 237 277 261 228 234 225 232 245 Assuming that the data come from independent normal populations with equal variance. Con-struct a 90% confidence interval for the dierence of the two population means. Is there evidence that wage incentives through commission yield greater average sales volume? 8. High blood pressure (hypertension) is a leading cause of strokes. Medical researchers are con-stantly seeking ways to treat patients suering from this condition. A specialist in hypertension claims that regular aerobic exercise can reduce high blood pressure just as successfully as drugs, with none of the adverse side eects. To test this claim, 30 patients who suer from hypertension were chosen to participate in an experiment. For 60 days, 16 patients exercised three time per week for one hour (Group 1); and the other 14 patients took the standard medication (Group 2). The percentage reduction in blood pressure was recorded for each individual, and the following summary statistics were obtained: x1 = 13:2; x2 = 9:51; s1 = 2:68; s2 = 3:61: Construct a 95% confidence interval for the dierence of the population mean percentage reduc-tion in blood pressure between the two treatment groups. Telemarketers obtain names and telephone numbers from several sources. To determine whether one particular source is better than a second, random samples of 400 and 420 names and numbers were obtained from sources A and B, respectively of which 52 and 46 from A and B made a purchase. Construct a 99% confidence interval for pA pB, the dierence in the proportions of customers making a purchase from the two sources. THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1306/STAT1603 Introductory Statistics (2015-2016) Assignment 5 Hand in Questions 4, 5, 8 and 9 on or before November 30, 2015 A plaque beside an elevator reads \"Capacity: 950 pounds, 6 persons\". Assume the weights of people entering the elevator are independently and identically distributed with = 150 pounds and standard deviation = 30 pounds. A person is carrying a suitcase that weighs exactly five times his own weight. What is the probability that the weight limit is exceeded? If there are six people in the elevator, what is the probability that the weight limit is exceeded? Repeat (b) if seven people crowd in. What would be the answer to (c) if you are one of the seven and your weight is 135 pounds? A paint manufacturer wants to determine the average drying time of a new interior wall paint. In 12 test areas of equal size, he obtained a mean drying time of 66.3 minutes and a standard deviation of 8.4 minutes. Construct a 95% confidence interval for the true mean drying time. What assumption is needed in order to carry out the appropriate estimation procedure? A random sample of 6 students in a physical education class had their pulse rates (beats per minute) measured before and after the 50-yard dash, with the following results: Student 1 2 3 4 5 6 Before 74 87 74 96 95 82 After 83 96 97 110 122 96 Construct a 95% confidence interval for the mean increase in pulse rate. Also construct a 90% confidence interval for the population standard deviation for the increase in pulse rate. A process producing bricks is known to give an output whose weights are normally distributed with population standard deviation 0.12 kg. A random sample of sixteen bricks from today's output had a mean weight of 4.07 kg. Find a 99% confidence interval for the mean weight of all bricks produced this day. It is decided that a sample of twenty bricks will be taken tomorrow. Without doing the calculations, state whether a 99% confidence interval for the mean weight of tomorrow's output would be wider than, narrower than or the same width as that found in (a). How many more bricks should be sampled so that the sample mean will be within 0.01 kg of the population mean with a probability of at least 0.99? A study is being made to estimate the proportion of voters in a sizeable community who favor the construction of a nuclear power plant. If it is found that only 140 of 400 voters selected at random favor the project, find a 95% confidence interval for the proportion of all voters in this community who favor the project. STAT1306/1603: Assignment 5 2 To determine which of the two types of seeds was better, a state agricultural station chose 9 two-acre plots of land randomly within the state. Each plot was split in half, and a coin was tossed to determine in an unbiased way which half would be sown with seed A, and which half with seed B. The yields, in bushels, were recorded as follows: County P Q R S T U V H K Seed A 82 68 154 93 78 148 89 74 98 Seed B 89 69 173 91 81 150 97 64 117 Which seed is better? To back up your answer, construct an appropriate 95% confidence interval and state the assumptions required. 7. An industrial psychologist wishes to study the eects of motivation on sales in a particular firm. Of 24 new salespersons, 12 are paid an hourly rate (Group A) and 12 are paid a commission (Group B). The 24 individuals are randomly assigned to the two groups. The following data represent the sales volume (in thousands of dollars) achieved during the first month on the job. Hourly Rate 256 239 222 207 228 241 212 216 236 219 225 230 Commission 224 254 273 285 237 277 261 228 234 225 232 245 Assuming that the data come from independent normal populations with equal variance. Con-struct a 90% confidence interval for the dierence of the two population means. Is there evidence that wage incentives through commission yield greater average sales volume? 8. High blood pressure (hypertension) is a leading cause of strokes. Medical researchers are con-stantly seeking ways to treat patients suering from this condition. A specialist in hypertension claims that regular aerobic exercise can reduce high blood pressure just as successfully as drugs, with none of the adverse side eects. To test this claim, 30 patients who suer from hypertension were chosen to participate in an experiment. For 60 days, 16 patients exercised three time per week for one hour (Group 1); and the other 14 patients took the standard medication (Group 2). The percentage reduction in blood pressure was recorded for each individual, and the following summary statistics were obtained: x1 = 13:2; x2 = 9:51; s1 = 2:68; s2 = 3:61: Construct a 95% confidence interval for the dierence of the population mean percentage reduc-tion in blood pressure between the two treatment groups. Telemarketers obtain names and telephone numbers from several sources. To determine whether one particular source is better than a second, random samples of 400 and 420 names and numbers were obtained from sources A and B, respectively of which 52 and 46 from A and B made a purchase. Construct a 99% confidence interval for pA pB, the dierence in the proportions of customers making a purchase from the two sources. THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1306/STAT1603 Introductory Statistics (2015-2016) Assignment 5 Hand in Questions 4, 5, 8 and 9 on or before November 30, 2015 A plaque beside an elevator reads \"Capacity: 950 pounds, 6 persons\". Assume the weights of people entering the elevator are independently and identically distributed with = 150 pounds and standard deviation = 30 pounds. A person is carrying a suitcase that weighs exactly five times his own weight. What is the probability that the weight limit is exceeded? If there are six people in the elevator, what is the probability that the weight limit is exceeded? Repeat (b) if seven people crowd in. What would be the answer to (c) if you are one of the seven and your weight is 135 pounds? A paint manufacturer wants to determine the average drying time of a new interior wall paint. In 12 test areas of equal size, he obtained a mean drying time of 66.3 minutes and a standard deviation of 8.4 minutes. Construct a 95% confidence interval for the true mean drying time. What assumption is needed in order to carry out the appropriate estimation procedure? A random sample of 6 students in a physical education class had their pulse rates (beats per minute) measured before and after the 50-yard dash, with the following results: Student 1 2 3 4 5 6 Before 74 87 74 96 95 82 After 83 96 97 110 122 96 Construct a 95% confidence interval for the mean increase in pulse rate. Also construct a 90% confidence interval for the population standard deviation for the increase in pulse rate. A process producing bricks is known to give an output whose weights are normally distributed with population standard deviation 0.12 kg. A random sample of sixteen bricks from today's output had a mean weight of 4.07 kg. Find a 99% confidence interval for the mean weight of all bricks produced this day. It is decided that a sample of twenty bricks will be taken tomorrow. Without doing the calculations, state whether a 99% confidence interval for the mean weight of tomorrow's output would be wider than, narrower than or the same width as that found in (a). How many more bricks should be sampled so that the sample mean will be within 0.01 kg of the population mean with a probability of at least 0.99? A study is being made to estimate the proportion of voters in a sizeable community who favor the construction of a nuclear power plant. If it is found that only 140 of 400 voters selected at random favor the project, find a 95% confidence interval for the proportion of all voters in this community who favor the project. STAT1306/1603: Assignment 5 2 To determine which of the two types of seeds was better, a state agricultural station chose 9 two-acre plots of land randomly within the state. Each plot was split in half, and a coin was tossed to determine in an unbiased way which half would be sown with seed A, and which half with seed B. The yields, in bushels, were recorded as follows: County P Q R S T U V H K Seed A 82 68 154 93 78 148 89 74 98 Seed B 89 69 173 91 81 150 97 64 117 Which seed is better? To back up your answer, construct an appropriate 95% confidence interval and state the assumptions required. 7. An industrial psychologist wishes to study the eects of motivation on sales in a particular firm. Of 24 new salespersons, 12 are paid an hourly rate (Group A) and 12 are paid a commission (Group B). The 24 individuals are randomly assigned to the two groups. The following data represent the sales volume (in thousands of dollars) achieved during the first month on the job. Hourly Rate 256 239 222 207 228 241 212 216 236 219 225 230 Commission 224 254 273 285 237 277 261 228 234 225 232 245 Assuming that the data come from independent normal populations with equal variance. Con-struct a 90% confidence interval for the dierence of the two population means. Is there evidence that wage incentives through commission yield greater average sales volume? 8. High blood pressure (hypertension) is a leading cause of strokes. Medical researchers are constantly seeking ways to treat patients suering from this condition. A specialist in hypertension claims that regular aerobic exercise can reduce high blood pressure just as successfully as drugs, with none of the adverse side eects. To test this claim, 30 patients who suer from hypertension were chosen to participate in an experiment. For 60 days, 16 patients exercised three time per week for one hour (Group 1); and the other 14 patients took the standard medication (Group 2). The percentage reduction in blood pressure was recorded for each individual, and the following summary statistics were obtained: x1 = 13.2; x2 = 9.51; s1 = 2.68; s2 = 3.61: Construct a 95% confidence interval for the dierence of the population mean percentage reduc-tion in blood pressure between the two treatment groups. Telemarketers obtain names and telephone numbers from several sources. To determine whether one particular source is better than a second, random samples of 400 and 420 names and numbers were obtained from sources A and B, respectively of which 52 and 46 from A and B made a purchase. Construct a 99% confidence interval for pA-pB, the dierence in the proportions of customers making a purchase from the two sources