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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 are and since then the null hypothesis of equal variances is not rejected.
Based on the information provided, the significance level is and the degrees of freedom are assuming that the population variances are equal.
Hence, it is found that the critical value for this two-tailed test for degrees of freedom is
Since the population variances are assumed to be equal, we need to compute the pooled standard deviation, as follows:
Since we assume that the population variances are equal, the standard error is computed as follows:
Now, we finally compute the confidence interval:
Therefore, based on the data provided, the 95% confidence interval for the difference between the population means is which indicates that we are 95% confident that the true difference between population means is contained by the interval