9.20 Gender bias in selecting managers For a large supermarket chain in Florida, a women’s group claimed that female employees were passed over for management training in favor of their male colleagues. The company denied this claim, saying it picked the employees from the eligible pool at random to receive this training. Statewide, the large pool of more than 1000 eligible employees who can be tapped for management training is 40% female and 60% male. Since this program began, 28 of the 40 employees chosen for management training were male and 12 were female.

a. The company claims that it selected employees for training according to their proportion in the pool of eligible employees. Define a parameter of interest and state this claim as a hypothesis. Explain why this hypothesis is a no-effect hypothesis.

b. State the null and alternative hypotheses for a test to investigate the strength of evidence to support the women’s claim of gender bias. (Hint: Gender bias means that either males or females are disproportionately selected.)

c. The table shows results of using MINITAB to do a large-sample analysis. Explain why the large-sample analysis is justified and show how software obtained the test statistic value.

d. To what alternative hypothesis does the P-value in the table refer? Use it to find the P-value for the significance test you specified in part b and interpret it.

e. What decision would you make for a 0.05 significance level? Interpret.

Transcribed Image Text:

Test of p = 0.4 vs p = 0.4 X N Sample p 12 40 0.300000 95% CI Z-Value P-Value (0.158, 0.442) -1.29 0.197 Using the normal approximation.