Question

A large university claims that the average cost of housing within 5 miles of the campus is $ 8900 per school year. A high school student is preparing her budget for her freshman year at the university. She is concerned that the university‘s estimate is too low. She obtains a random sample of 81 records and computes the average cost is $ 9050. Based on earlier data, the population standard deviation is $ 760. Use α=0.01 level of significance.

a) Step 1: State the null and alternative hypotheses.

b) Step 2: Write down the appropriate test statistic and the rejection region of your test (report zcritical(s))

c) Step 3: Compute the value of the test statistic (z observed)

d) Step 4: State your conclusion (in one sentence, state whether or not the test rejects the null hypothesis and in another sentence apply the results to the problem).

e) Compute the p- value for this test. Is the evidence strong or weak in supporting the alternative hypothesis?

Answer 1

Solution:

Conclusion : We reject the do not reject the null hypothesis and conclude that the average cost of housing within 5 miles of the campus is $ 8900 per school year.

Using the P-value approach: The p-value is p=0.0757, and since p=0.0757≥0.01, it is concluded that we have the weak evidence in supporting the alternative hypothesis?