Business and Economic Statistics II

Please answer the following questions. Write out each step we covered in class. Assisted-Living Facility Rent. Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increased 17% over the last five years to $3486. Assume this cost estimate is based on a sample of 120 facilities and from past studies it can be assumed that the population standard deviation is σ = $650. a. Develop a 90% confidence interval estimate of the population mean monthly rent. b. Develop a 95% confidence interval estimate of the population mean monthly rent. c. Develop a 99% confidence interval estimate of the population mean monthly rent. d. What happens to the width of the confidence interval as the confidence level is increased? Does this seem reasonable? Explain. Automobile Insurance Premiums. The average annual premium for automobile insurance in the United States is $1503. The following annual premiums ($) are representative of the website’s findings for the state of Michigan. 1905 3112 2312 2725 2545 2981 2677 2525 2627 2600 2370 2857 2962 2545 2675 2184 2529 2115 2332 2442 Assume the population is approximately normal. a. Provide a point estimate of the mean annual automobile insurance premium in Michigan. b. Develop a 95% confidence interval for the mean annual automobile insurance premium in Michigan. c. Does the 95% confidence interval for the annual automobile insurance premium in Michigan include the national average for the United States? What is your interpretation of the relationship between auto insurance premiums in Michigan and the national average? Federal Tax Returns. According to the IRS individuals filing federal income tax returns prior to March 31 received an average refund of $1056 in 2018. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). a. A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of will 𝐻0support the researcher’s contention. b. For a sample of 400 individuals who filed a tax return between April 10 and 15 the sample mean refund was $910. Based on prior experience a population standard deviation of σ = $1600 may be assumed. What is the p-value? c. At what is your conclusion?𝛼=.05 d. Repeat the preceding hypothesis test using the critical value approach. Price of Good Red Wine. According to the Vivino website the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England–based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence and it has collected prices for 56 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12 respectively

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