A state hospital system wants to evaluate the salaries of its obstetricians to ensure there is no gender inequality. The system randomly selects 20 obstetricians, 10 men and 10 women, and noted their salary. Use this information to answer questions 5-9.
Obstetrician Salaries
Women
- 241,649
- 292,508
- 177,973
- 302,631
- 240,740
- 330,995
- 394,437
- 293,739
- 328,970
- 346,404
Me?n
- 358,474
- 341,123
- 298,762
- 299,473
- 391,191
- 266,833
- 343,028
- 216,698
- 288,741
- 381,053
Conduct the following hypothesis test:
- A two-tail T-test for a two-sample difference in means at the 95% confidence level
- With Null Hypothesis that the men's salaries and women's salaries are equal
- And with Alternate Hypothesis that the men's salaries and women's salaries are unequal
1. Calculate the mean and standard deviation of the salaries for each group.
2. Using the correct degrees of freedom (df = # of men + # of women - # of groups), the correct number of tails, and at the correct confidence level, determine the critical value of t.
3. Explain under which scenarios using a pooled variance be inadvisable, then, calculate the pooled variance (formula for S2 is onpage 379) for the groups.
4. Calculate the test statistic, Ttest (formula for t is on page 380).
5. The state system's statistician tells you that the p-value for the test is 0.1089. Summarize the result of the study. Compare the mean salaries in each group. Compare the test statistic to the critical value. Compare the p-value to alpha. Do you find a statistically significant difference between men salaries and women salaries for obstetricians in the state hospital system? Is there a meaningful/practical difference? Explain your decisions and Justify your claims.