10.20 Annual income of CEOs A study analyzes the total annual pay of CEOs (in pounds) for a sample of UK companies over the period 2003–2006 categorized according to the number of compensation consultants employed. The sample included 311 firms having one consultant and 203 firms having two consultants. Software output shows the following results:

Two sample T hypothesis test:

μ1 : Mean of CEO total pay in firms with one compensation consultant

μ2 : Mean of CEO total pay in firms with two compensation consultants

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1 M2 Ho - 1 HA - 1 Difference between two means M2 = 0 12 Sample Statistics: 0 Sample N Mean Std. Dev. Population 1 311 1658 1314 Population 2 203 1779 1461 Hypothesis test results: Sample Std. Difference Diff. Err. DF T-Stat P-value 1 - 2 -121 126.75 399.12 -0.95 0.34 (Source: http://www.globalequity.org/geo/sites/default/files/ SSRN-id1646926.pdf) a. Does it seem plausible that income has a normal dis- tribution for each firms' category? Explain. b. What effect does the answer to part a have on infer- ence comparing population means? What assumptions are made for the inferences in this table? c. A 95% confidence interval for the difference in the population means for CEOs (men and women) is (-370.19, 128.19). Interpret, indicating the relevance of 0 falling in the interval.