Question

A survey question of men and women workers asked if they expected to receive a raise or promotion during the upcoming year. Two hundred men and 200 women were sampled. Of the men, 110 said yes but only 90 of the women said yes. Develop the hypotheses and test at 95% confidence to see if the percentage of women expecting to receive a raise or promotion is less than that of the men. What is your conclusion? Please show your work legibly.

Answer 1

The null and alternate hypothesis are:

H0:

Ha:

The test statistic is given by:

Since this is a right-tailed test, so the p-value is given by:

Since p-value is less than 0.05, so we have sufficient evidence to reject the null hypothesis H0 at 95% confidence.

Thus we can conclude that the percentage of women expecting to receive a raise or promotion is less than that of the men.