Question

An entrepreneur owns some land that he wishes to develop. He identifies two development options: build condominiums or build apartment buildings. Accordingly, he reviews public records and derives the following summary measures concerning annual profitability based on a random sample of 32 for each such local business ventures. For the analysis, he uses a historical (population) standard deviation of $22,800 for condominiums and $19,800 for apartment buildings. (You may find it useful to reference the appropriate table: z table or t table) Sample 1 represents condominiums and Sample 2 represents apartment buildings. Condominiums Apartment Buildings x⎯⎯1 x ¯ 1 = $243,500 x⎯⎯2 x ¯ 2 = $235,200 n1 = 32 n2 = 32 a. Set up the hypotheses to test whether the mean profitability differs between condominiums and apartment buildings. H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0 H0: μ1 − μ2 ≥ 0; HA: μ1 − μ2 < 0 H0: μ1 − μ2 ≤ 0; HA: μ1 − μ2 > 0

Answer 1

The question is to test if the mean profitability differs between condominiums and apartment buildings . Therefore, the hypothesis test should be:

In order to test this hypothesis, we can compute the test statistic:

where the sample values are as given in the problem. Based on the given p-value, we find the critical value and reject the null hypothesis if .

If the question was to test if the profitability of condominiums is greater than apartment buildings , then the hypothesis test would be:

More generally, if the question is to test if situation X hold, then the hypothesis test is

NOT X