Question

A sample of n = 9 scores is obtained from a normal population distribution with σ = 12. The sample mean is M = 60.

a. With a two-tailed test and α = .05, use the sample data to test the hypothesis that the population mean is μ = 65.

b. With a two-tailed test and α = .05, use the sample data to test the hypothesis that the population mean is μ = 55.

c. In parts (a) and (b) of this problem, you should find that μ = 65 and μ = 55 are both acceptable hypotheses. Explain how two different values can both be acceptable.

Answer 1

a. vs

Here the value of the test statistic is

Now at 5% level of significance, the critical value of this test is 1.96.

So, here |Z| < 1.96.

Hence we can't have enough evidence to reject the null hypothesis or we can accept the null hypothesis.

b. vs

Here the value of the test statistic is

Now at 5% level of significance, the critical value of this test is 1.96.

So, here |Z| < 1.96.

Hence we can't have enough evidence to reject the null hypothesis or we can accept the null hypothesis.

c. The test is two-sided, this is why we are considering |Z|. In both of the cases, the absolute value of the test statistics is less than the critical value. But if the tests are right-tailed or left-tailed for both of the cases then one null hypothesis should be rejected.