# Statistics

16. The employee benefits manager of a small private university would like to estimate the proportion of full time employees who like to adopt the first (i.e. plan A) of three available health care plans in the coming enrolment period. A reliable frame of the universities employees and their tentative healthcare preferences are given on the spreadsheet labeled (Question 16/18)

a. Use excel to choose a simple random sample of size 45 from the given frame

b. Using the sample found in part A, construct a 99% confidence interval for the proportion university employees who prefer plan A. Assume that the population consists of the preferences of all employees in the given frame.

c. Interpret the 99% confidence interval constructed in part B.

18. Continuing problem 16, select simple random samples of 30 individuals from each given employee classifications (i.e. administrative staff and faculty). Construct a 99% confidence interval for the proportion of employees who prefer adopting plan A for each of the three classifications. Do you see evidence of significant differences among these three interval estimates? Summarize your findings

26. Consider a random sample from 100 households is a middle class neighborhood that was the recent focus of an economic development study conducted by the local govt. Specifically, for each of the 100 households, information was gathered on each of the following variables: family size, location of whether those surveyed owned or rented their home, gross annual income of this first household wage earner ( if applicable) , monthly home mortgage or rent, average expenditures on utilities, and the total indebtedness (excluding the value of a home mortgage) of the household. That data is provided on spread sheet titled (prob 26)

a. Separate the households in the sample by location of their residence within the given community. For each of the 4 locations, use the sample information to generate a 90% confidence interval for the mean annual income of all relevant first household wage earners. Compare these 4 interval estimates. You may also want to consider generating box plots of the primary wage earner variable for households in each of the 4 given locations.

b. Generate a 90% confidence interval for the difference between the mean annual income levels of the first household wage earners in the first (i.e. SW) and second (i.e. NW) sectors of the community. Generate similar 90% confidence intervals for the differences between the mean annual income levels of primary wage earners from all other pairs of locations (i.e. first & third, first & fourth, second and third, second and fourth, and third and fourth) summarize your findings

6. A study is performed in a large southern town to determine whether the average weekly grocery bill per four person family in the town is significantly different from the national average. A random sample of the weekly grocery bills of four person families in this town can be found on spreadsheet labeled (problem 6)

a. Assume that the national average weekly grocery bill for a four person family is $100. Is the sample evidence statistically significant? If so, at what significance levels can you reject the null hypothesis?

b. For which values if the sample mean (i.e. average weekly grocery bill) would you decide to reject the null hypothesis at alpha =0.01 significance level? For which values of the sample mean would you decide to reject the null hypothesis at the alpha =0.10 level?

44. A finance professor has just given a midterm exam in her corporate finance course. In particular she is interested in determining whether the distribution of 100 exam scores is normally distributed. The data is spreadsheet labeled (problem 44). Perform a chi-square goodness of fit test. Report and interpret the computed p value. What can you conclude about normality?

#### Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems in EXCEL and provides students with a clear perspective of the underlying concepts.