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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 degrees of freedom, degrees of freedom, are and and since then the null hypothesis of equal variances is 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.
Based on the information provided, the significance level is and the degrees of freedom are computed as follows, assuming that the population variances are unequal:
Hence, it is found that the critical value for this two-tailed test is for and
The rejection region for this two-tailed test is
Since it is assumed that the population variances are unequal, the t-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is rejected.
Using the P-value approach: The p-value for two-tailed is and since it is concluded that the null hypothes is rejected.
Therefore, there is enough evidence to claim that the population mean is different than at the significance level.