Question

Salary ($)	Master's Degree (1 = Yes)
61,500	0
69,200	0
76,000	0
78,700	0
81,500	0
83,800	0
84,200	0
84,300	0
85,400	1
87,200	0
88,700	0
90,700	1
97,200	0
97,600	1
99,900	1
100,000	1
101,800	1
102,700	1
103,400	0
111,300	1

Do NOT use the “finite population” corrections for standard deviation calculation in this problem. Just assume we’re dealing with an infinite population.

1. Provide the formal null and alternative hypotheses for a hypothesis test of the question of whether or not the mean administrator salary is really $84,000.

Assume that the underlying population of administrator salaries is normally distributed.

1. b.Conduct this hypothesis test based on the 95% significance level. What is the p-value? Do you reject or fail to reject your null hypothesis? Why?
2. c. Create a 90% confidence interval for the mean administrator salary. Explain in a sentence, in layman’s terms, what this confidence interval implies.
3. d. Compare your hypothesis test in part “b” to your confidence interval in part “c”. Do these results conflict with each other? (i.e., is it OK to find these two answers simultaneously?...if so, why?...OR, is there a conflict where it should be impossible for these results to occur simultaneously?)

Answer 1

We are 90% confident that the true mean administrator salary will lie between $84391 and $94119, that is, there is a 90% chance of the true mean administrator salary lying within this range.

(d) Yes, it is OK to conduct the hypothesis test and finding the confidence interval. Here the hypothesis test and the confidence interval are yielding the same results, that is, the true mean administrator salary is not really $84000. It is more than that.