MATH 534 Week 4 Quiz

1. Question: Suppose a random sample of 400 is selected from a population with a standard deviation of 5. If the sample mean is 25, the 98% confidence interval to estimate the population mean is between ________. 2. Question: The point estimate of the population mean is _________. 3. Question: Suppose a random sample of 50 is drawn from a population whose standard deviation is unknown. If the sample mean is 70 and the sample standard deviation is 5, the 92% confidence interval to estimate the population mean is between _____________. 4. Question: Suppose a researcher is interested in understanding the variation in the price of store brand milk. A random sample of 36 grocery stores selected from a population and the mean price of store brand milk is calculated. The sample mean is $3.13 with a population standard deviation of $0.23. Construct a 92% confidence interval to estimate the population mean. 5. Question: Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Accordingly, his staff recorded the waiting times for 64 randomly selected walk-in customers and determined that their mean waiting time was 15 minutes. Assume that the population standard deviation is 4 minutes. The 90% confidence interval for the population mean of waiting times is ________. 6. Question: James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. His staff randomly selected personnel files for 100 tellers in the Southeast Region and determined that their mean training time was 25 hours. Assume that the population standard deviation is 5 hours. The 88% confidence interval for the population mean of training times is ____ 7. Question: A department store finds that in a random sample of 200 customers, 60% of the sampled customers had browsed its website prior to visiting the store. Based on this data, a 90% confidence interval for the population proportion of customers that browse the store’s website prior to visiting the store will be between _________. 8. Question: A researcher is interested in estimating the mean weight of a semi tracker truck to determine the potential load capacity. She takes a random sample of 17 trucks and computes a sample mean of 20,000 pounds with sample standard deviation of 1,500. The 90% confidence interval for the population mean rod length is __________. 9. Question: Life tests performed on a sample of 13 batteries of a new model indicated: (1) an average life of 75 months, and (2) a standard deviation of 5 months. Other battery models, produced by similar processes, have normally distributed life spans. The 98% confidence interval for the population mean life of the new model is _____________. 10. Question: Suppose you want to estimate a population mean correct to within 0.25 with probability equal to 0.95. You do not know the population variance but you are given that the observations will range in value between 20 and 40. Then the approximate sample size that will produce the desired accuracy of the estimate is ____________. 11. Question: Construct 90%, 95%, and 99% confidence intervals to estimate μ from the following data. State the point estimate. Assume the data come from a normally distributed population. 12. Question: A large national company is considering negotiating cellular phone rates for its employees. The Human Resource department would like to estimate the proportion of its employee population who own an Apple iPhone. A random sample of size 250 is taken and 40% of the sample own and iPhone. The 95% confidence interval to estimate the population proportion is __________. 13. Question: A large trucking company wants to estimate the proportion of its trailer truck population with refrigerated carrier capacity. A random sample of 200 trailer trucks is taken and 30% of the sample have refrigerated carrier capacity. The 90% confidence interval to estimate the population proportion is _________. 14. Question: Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 randomly selected Americans. Suppose 716 of the sampled people replied that the environment is a major issue with them. Construct a 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them. What is the point estimate of this proportion? 15. Question: A study is going to be conducted in which a population mean will be estimated using a 92% confidence interval. The estimate needs to be within 12 of the actual population mean. The population variance is estimated to be around 2500. The necessary sample size should be at least _______. 16. Question: A study is going to be conducted in which a mean of a lifetime of batteries produced by a certain method will be estimated using a 90% confidence interval. The estimate needs to be within +/- 2 hours of the actual population mean. The population standard deviation σ is estimated to be around 25 hours. The necessary sample size should be at least ____________.