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Instructions: Complete each problem on a separate worksheet in a single Excel file. Rename the separate worksheets with the respective problem number. You may have to copy and paste the datasets into your homework file first. Name the file with your last name, first initial, and HW #5. Label each part of the question. When calculating statistics, label your outputs. Submit your completed file in Blackboard.

1. A drugstore manager needs to purchase adequate supplies of various brands of toothpaste to meet the ongoing demands of its customers. In particular, the company is interested in estimating the proportion of customers who favor the country’s leading brand of toothpaste: Crest. In the file 310homework5data.xlsx, problem #1 data contains the toothpaste brand preferences of 200 randomly selected customers, obtained recently through a customer survey. Calculate a 95% confidence interval for the proportion of all of the company’s customers who prefer Crest toothpaste. How might the manager use this confidence interval for purchasing decisions?

2. The employee benefits manager of a large public university would like to estimate the proportion of full-time employees who prefer adopting the first (Plan A) of three available health care plans in the next annual enrollment period. A random sample of the university’s employees and their tentative healthcare preferences are in the file 310homework5data.xlsx in Problem #2.

a. Calculate a 90% confidence interval for the proportion of all university employees who favor Plan A.

b. The file also includes the classification of each employee (administrative staff, support staff, or faculty). Calculate a separate 90% confidence interval for each of these groups for the proportion who favors plan A. How do these confidence intervals compare to one another?

3. Elected officials in a California city are preparing the annual budget for their community. They would like to estimate how much their constituents living in this city are typically paying each year in real estate taxes. Given that there are over 100,000 homeowners in this city, the officials have decided to sample a representative subset of taxpayers and study their tax payments.

a. What sample size is required to generate a 95% confidence interval for the mean annual real estate tax payment with a half-length (margin of error) of $100? Assume that the best estimate of the population standard deviation is $535.

b. If a random sample of the size from part a is selected and a 95% confidence interval for the mean is calculated, will the margin of error be equal to $100? Why or why not?

c. Now, suppose that the officials want to construct a 95% confidence interval with margin of error of $75. What sample size is required? Assume the same standard deviation as in part a.

d. If the city officials want to determine the proportion of taxpayers that pay their taxes, how many residents will they need to survey if they want to margin of error to be 1%?

4. You are trying to estimate the average amount a family spends on food during a year. In the past, the standard deviation of the amount a family has spent on food during a year is approximately $1000. If you want to be 99% sure you have estimated average family expenditures within $50, how many families do you need to survey?