IMA’s 2021 survey. For many years, the Institute of Management Accountants (IMA) has conducted a very popular survey of the salaries of its global members, enabling them to compare their compensation to others, assess the value of education and certification, and more. The IMA’s 2021 survey analyzes information gathered from respondents located in the Middle East, Africa, and India (MEAI) region and also includes a separate, brief summary of responses from India and Egypt. The following table shows the mean compensation of male and female members retrieved from the survey report. Female Male Sample size 132 527 Mean of the total compensation ($) 32,994 45,661

a. Based on the information given, why is it impossible to provide a measure of reliability for the inference “The female total compensation, on average, is less than the male total compensation”?

b. What information do you need to obtain a measure of reliability for the inference, part a?

c. Give a value of the test statistic that would lead you to conclude that the true mean of the total compensation of females is less than the true mean of the total compensation of males if you are willing to risk a Type I error rate of .01.

d. Assume that s, the standard deviation of the total compensation, is the same for both given genders. Give an estimate of s that would lead you to conclude that the true mean of total compensation of females is less than the true mean of total compensation of males using a = .01.

e. Is the true value of s likely to be larger or smaller than the one you calculated in part d?