The national mean annual salary for a school administrator is $90,000 a year (The Cincinnati Enquirer, April 7, 2012). A school official took a sample of 25 school administrators in the state of Ohio to learn about salaries in that state and to see if they differed from the national average.

a. Formulate hypotheses that can be used to determine whether the population mean annual administrator salaries in Ohio differ from the national mean of $90,000.

Null hypothesis:

1. H ₀ : µ = 90,000

2. H ₀ : µ ¹ 90,000

3. H ₀ : µ < 90,000

Alternative hypothesis:

1. H _a : µ ¹ 90,000

2. H _a : µ = 90,000

3. H _a : µ < 90,000

b. Use the sample data for the 25 Ohio administrators and the t distribution table (Table 2 in Appendix B) to estimate a p-value range for your hypothesis test in part (a).
c. At = .05, can your null hypothesis be rejected? What is your conclusion?

d. Repeat the preceding hypothesis test using the critical value approach.