Question

A female employee at a nearby hospital is convinced that male physicians are earning significantly more of an annual salary than female physicians. In order to test the hypothesis that male physicians earn more than $15,000.00 on the average than females, the employee gathers a SRS of male and female physicians at the health center. Assume the following table summarizes the descriptive statistics for the two groups.

Gender	Average Annual Income	Standard Deviation	Sample Size
Female	$126,000.00	4,673.00	24
Male	$192,000.00	3,698.00	28

A) Carry out the appropriate statistical procedure to test the employee’s hypothesis at the alpha=0.05 level. Do not assume equal variances. Carefully write out your null and alternative hypotheses, and interpret your results.

B) Construct a 95% confidence interval about your point estimate for the difference in annual income by gender. Provide an interpretation for your confidence interval.

		A) Ho: µ1=µ2 Ha: µ1<µ2 T statistic=56.81 Pvalue~0 Accept the Ho that men and women employed by the hospital earn, on the average, the same annual income. B) (70384, 73616) We are 95% confident that the true average difference in annual salary between women and men lies within the interval.
		A) Ho: µ1=µ2 Ha: µ1<µ2 T statistic=-105.18 Pvalue~0 Reject the Ho that men and women employed by the hospital earn, on the average, the same annual income. Instead, reject the null hypothesis in favor of the alternative, that females earn significantly less than their male counterparts on the average. B) (-88384, -83616) We are 95% confident that the true average difference in annual salary between women and men lies within the interval.
		A) Ho: µ1=µ2 Ha: µ1<µ2 T statistic=-55.81 Pvalue~0 Reject the Ho that men and women employed by the hospital earn, on the average, the same annual income. Instead, reject the null hypothesis in favor of the alternative, that females earn significantly less than their male counterparts on the average. B) (-68384, -63616) We are 95% confident that the true average difference in annual salary between women and men lies within the interval.

Answer 1

Here our testing problem is

vs

The p value of the test is very close to 0.

So null hypothesis is rejected. That is the average salary of male is higher than salary of the females.

From the confidence interval we are 95% confident that the difference of salary between females and males will lie within (-68384,-63616)

So this indicates males earn minimum 63616 more than the females.

So the claim that males earn more than 15000 from females is true.