In a 1982 racial discrimination lawsuit, the court accepted the defendant’s argument that racial differences in hiring and promotion should be separated into eight job categories

[36]. In hiring, it turned out that blacks were underrepresented by statistically significant amounts (at the 5 percent level) in four of the eight job categories. In the other four categories, whites were underrepresented in two cases and blacks were underrepresented in two cases, though the differences were not statistically significant at the 5 percent level. The court concluded that four of eight categories was not sufficient to establish a prima facie case of racial discrimination. Assume that the data for these eight job categories are independent random samples.

a. What is the null hypothesis?

b. Explain why data that are divided into eight job categories might not show statistical significance in any of these job categories, even though there is statistical significance when the data are aggregated.

c. Explain why data that are divided into eight job categories might show statistical significance in each of the eight categories, even though there is no statistical significance when the data are aggregated.