The file P07_02.xlsx contains data on the 1995 students who have gone through the MBA program at State University. You can consider this the population of State University’s MBA students.
a. Find the mean and standard deviation for each of the numerical variables in this population. Also, find the following proportions: the proportion of students who are male, the proportion of students who are international (not from the USA), the proportion of students under 30 years of age, and the proportion of students with an engineering undergrad major.
b. Using the method in this section (not StatTools), generate a simple random sample of 100 students from this population, and find the mean and standard deviation of each numerical variable in the sample. Is there any way to know (without the information in part a) whether your summary measures for the sample are lower or higher than the (supposedly unknown) population summary measures?
c. Use StatTools to generate 10 simple random samples of size 100. For each, find the mean of School Debt and its deviation from the population mean in part a (negative if it is below the population mean, positive if it is above the population mean). What is the average of these 10 deviations? What would you expect it to be?
d. We want random samples to be representative of the population in terms of various demographics. For each of the samples in part c, find each of the proportions requested in part a. Do these samples appear to be representative of the population in terms of age, gender, nationality, and undergrad major? Why or why not? If they are not representative, is it because there is something wrong with the sampling procedure?