Question

For the data below determine if the variances are not equal. Use the six steps of hypothesis testing at a 0.10 level of significance.

_x1 = 84, s₁ = 10, n = 30

_x2 = 85, s₂ = 12, n = 25

Answer 1

The corresponding sample variances are:

s1²=10²=100

s2²=12²=144

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:

Ha:

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 α=0.10, and the the rejection region for this two-tailed test is R={F:F<0.526 or F>1.945}.

(3) Test Statistics

The provided sample variances are and and the sample sizes are given by n1​=30 and

n2​=25.

The F-statistic is computed as follows:

(4) Decision about the null hypothesis

Since from the sample information we get that FL​=0.526<F=0.694<FU​=1.945, 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 variance is different than the population variance ​, at the α=0.10 significance level.

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