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A F-test is used to test for the equality of variances. The following F-ratio is obtained:
The critical values for two-tailed, are and and since then the null hypothesis of equal variances is not rejected.
The following null and alternative hypotheses need to be tested:
This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.
The significance level is and the degrees of freedom are
Hence, it is found that the critical value for this two-tailed test, and is
The rejection region for this two-tailed test is
Since it is assumed that the population variances are equal, the t-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is not rejected.
Using the P-value approach:
The p-value for two-tailed, degrees of freedom, is and since it is concluded that the null hypothes is not rejected.
Therefore, there is not enough evidence to claim that the population mean is different than at the significance level.