Question

Two independent random samples were selected from two normally distributed populations with means and variances (μ1,σ21) and (μ2,σ22). The sample sizes, means and variances are shown in the following table.

Sample 1 n1 = 13 x̄1 = 18.2 s21 = 75.3

Sample 2 n2 = 14 x̄2 = 17.1 s2= 61.3

(a). Test H0 : σ12 = σ2against Ha : σ12 ̸= σ2. Use α = 0.05. Clearly show the 4 steps.

(b). TestH0 :μ1 −μ2 =0againstHa :μ1 −μ2 >0. Useα=0.05. Clearlyshowthe4steps.

Answer 1

sample 1:

Sample 2:

a) Here we have to do equality test for two population standard deviation

This is similar to testing the population variance, as the standard deviation is square of variance.

This corresponds to a two-tailed test, for which a F-test for two population variances needs to be used.

(2) Rejection Region

Based on the information provided, the significance level is , and the the rejection region for this two-tailed test is

(3) Test Statistics:

The F-statistic is computed as follows:

(4) The decision about the null hypothesis

Since from the sample information we get that , it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population standard deviation    is different than the population variance , at tthe significance level.

b)