week-10-practice-quiz-with-explanation-and-correct-answer

1. Award: 10 out of 10.00 points 2. Award: 10 out of 10.00 points Score: 160/200 Points 80 % The fraction or ratio of a sample possessing a certain trait is called a: Population. Mean. Confidence interval. Proportion. Proportion is the same as fraction is the same as ratio is the same as percentage. References Multiple Choice Learning Objective: 08-03 Compute and interpret a confidence interval for a population mean when the population standard deviation is unknown. An economist wants to estimate the proportion of Canadians who own their homes. A random sample of 800 people reveals 544 own their homes. Develop a 95% confidence interval for the population proportion. 0.68 ± 0.053 0.68 ± 0.032 0.32 ± 0.032 0.68 ± 0.027 We have: x = 544 people, n = 800 people, 95% confidence interval For a 95% confidence interval z = 1.96. First calculate the sample proportion: So, we estimate 68% of people own their homes. The 95% confidence interval is . References Multiple Choice Learning Objective: 08-03 Compute and interpret a confidence interval for a population mean when the population standard deviation is unknown.    ✓   ✓   

3. Award: 10 out of 10.00 points 4. Award: 10 out of 10.00 points 5. Award: 10 out of 10.00 points When do we apply the finite population correction factor? When our sample size is 5% or more of our finite population size. When we know exactly what the population size is. Anytime we take a sample. Anytime we are calculating a sample size. References Multiple Choice Learning Objective: 08-06 Adjust a confidence interval for a finite population. We know the total population is 3,000. 30% of the 500 people sampled say that they prefer hot dogs to hamburgers. Prepare a 95% confidence interval for the proportion that prefer hot dogs. 26.00% to 34.00% prefer hot dogs. 26.33% to 33.67% prefer hot dogs. 16.67% Cannot be determined from the information provided. References Multiple Choice Learning Objective: 08-04 Compute and interpret a confidence interval for a population proportion. Learning Objective: 08-05 Calculate the required sample size to estimate a population mean or population proportion. The necessary sample size depends on: The level of confidence desired The allowable margin of error The variability in the population of study The level of confidence desired, the allowable margin of error, and the variability in the population of study. The necessary sample size depends on all three of the factors listed. References Multiple Choice Learning Objective: 08-06 Adjust a confidence interval for a finite population. ✓      ✓       ✓ 

8. Award: 10 out of 10.00 points 9. Award: 10 out of 10.00 points 10. Award: 10 out of 10.00 points American Express cardholders are reported to spend more per purchase than either VISA or MasterCard cardholders. The average purchase at a giftware store is $70. The owner conducts a random survey of 120 people who use their American Express card and finds 84 of them make purchases in excess of the average $70. Conduct a 90% confidence interval for the number of American Express cardholders that make purchases greater than $70. 0.70 ± 0.002 0.70 ± 0.003 0.70 ± 0.069 0.70 ± 0.042 We have: x = 84 cardholders, n = 120 cardholders, 90% confidence interval For a 90% confidence interval z = 1.645. First calculate the sample proportion: So, we estimate 70% of American Express cardholders spend in excess of the average purchase. The 90% confidence interval is . References Multiple Choice Learning Objective: 08-04 Compute and interpret a confidence interval for a population proportion. A finite population is: a large population. an exactly known population size. 5% of the total population. a population from which samples were taken. References Multiple Choice Learning Objective: 08-05 Calculate the required sample size to estimate a population mean or population proportion. Determining a sample size depends on all of these except: confidence level. population size. maximum allowable error. variation in the population. Determining sample size does not depend on the population size. Population size has no bearing on how large or small a sample size will be. If there is no prior estimate of the population proportion, we use p = 0.5 to maximize the sample size. References Multiple Choice Learning Objective: 08-06 Adjust a confidence interval for a finite population.   ✓    ✓     ✓   

11. Award: 10 out of 10.00 points 12. Award: 0 out of 10.00 points Past surveys reveal that 40% of Florida winter vacationers spend more than $3000 per month on accommodation. Florida tourism wants to update this information. Using the 90% confidence level and an error of 5%, what is the necessary sample size? 8 260 369 6495 n = (0.4)(1 − 0.4)(1.645/0.05)^2 = 259.8 References Multiple Choice Learning Objective: 08-06 Adjust a confidence interval for a finite population. Sixty items are randomly selected from a population of 900. The number of defective items is found to be 12. Develop a 95% confidence interval for the population proportion of defective items. (Round the final answers to 3 decimal places.) The confidence interval is between 0.097 and 0.303 . References Worksheet Learning Objective: 08-06 Adjust a confidence interval for a finite population. Sixty items are randomly selected from a population of 900. The number of defective items is found to be 12. Develop a 95% confidence interval for the population proportion of defective items. (Round the final answers to 3 decimal places.) The confidence interval is between 0.102 ± 0.001 and 0.298 ± 0.001 . Explanation: 0.102 to 0.298, found by  ✓   

15. Award: 10 out of 10.00 points 16. Award: 0 out of 10.00 points Previous surveys estimated that 15% of students use the college gym. The manager would like to verify this estimate within plus or minus 0.05. At a 95% level of confidence, how large a sample is required? (Round the final answer to the nearest whole number.) The sample size is 196 . References Worksheet Learning Objective: 08-05 Calculate the required sample size to estimate a population mean or population proportion. Previous surveys estimated that 15% of students use the college gym. The manager would like to verify this estimate within plus or minus 0.05. At a 95% level of confidence, how large a sample is required? (Round the final answer to the nearest whole number.) The sample size is 196 . Explanation: 196, found by The estimate of the population proportion is to be within plus or minus 0.10, with a 99% level of confidence. The best estimate of the population proportion is 0.45. How large a sample is required? (Round the final answer to the nearest whole number.) Sample size 184 References Worksheet Learning Objective: 08-05 Calculate the required sample size to estimate a population mean or population proportion. The estimate of the population proportion is to be within plus or minus 0.10, with a 99% level of confidence. The best estimate of the population proportion is 0.45. How large a sample is required? (Round the final answer to the nearest whole number.) Sample size 165 Explanation: 165, found by

17. Award: 10 out of 10.00 points 18. Award: 10 out of 10.00 points Suppose that the prime minister wants an estimate of the proportion of the population that supports his current policy on health care. The prime minister wants the estimate to be within 0.04 of the true proportion. Assume a 95% level of confidence. The prime minister’s political advisors estimated the proportion supporting the current policy to be 0.60. (Round the final answers to the nearest whole number.) a. How large a sample is required? 577 b. How large a sample would be necessary if no estimate were available for the proportion that supports current policy? 601 References Worksheet Learning Objective: 08-05 Calculate the required sample size to estimate a population mean or population proportion. Suppose that the prime minister wants an estimate of the proportion of the population that supports his current policy on health care. The prime minister wants the estimate to be within 0.04 of the true proportion. Assume a 95% level of confidence. The prime minister’s political advisors estimated the proportion supporting the current policy to be 0.60. (Round the final answers to the nearest whole number.) a. How large a sample is required? 577 b. How large a sample would be necessary if no estimate were available for the proportion that supports current policy? 601 Explanation: a. 577, found by b. 601, found by . Furniture Land surveyed 600 consumers and found that 414 were enthusiastic about a new home dècor it plans to show in its store in High Point. Construct the 99% confidence interval for the population proportion. (Round the final answers to 3 decimal places.) Confidence interval for the population proportion is 0.641 and 0.739 . References Worksheet Learning Objective: 08-04 Compute and interpret a confidence interval for a population proportion. Furniture Land surveyed 600 consumers and found that 414 were enthusiastic about a new home dècor it plans to show in its store in High Point. Construct the 99% confidence interval for the population proportion. (Round the final answers to 3 decimal places.) Confidence interval for the population proportion is 0.641 ± 0.001 and 0.739 ± 0.001 . Explanation: Between 0.641 and 0.739, found by

20. Award: 0 out of 10.00 points You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 95% confidence level and state that the estimated proportion must be within 2% of the population proportion. A pilot survey reveals that 5 of the 50 sampled hold two or more jobs. How many in the workforce should be interviewed to meet your requirements? (Round the final answer to the nearest whole number.) Number of persons to be interviewed 866 References Worksheet Learning Objective: 08-05 Calculate the required sample size to estimate a population mean or population proportion. You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 95% confidence level and state that the estimated proportion must be within 2% of the population proportion. A pilot survey reveals that 5 of the 50 sampled hold two or more jobs. How many in the workforce should be interviewed to meet your requirements? (Round the final answer to the nearest whole number.) Number of persons to be interviewed 865 Explanation: 865, found by 0.10(0.90) = 864.36