Final answer:
The F test for equality of two variances is used to determine homogeneity of variance within two independent groups, assuming normal distribution of the populations from which the samples are drawn.
Step-by-step explanation:
The test that helps determine whether we have homogeneity of variance within two independent groups is the F test for equality of two variances. This test assumes that the populations from which the samples are drawn are normally distributed. The test statistic used here is the ratio of the two sample variances, which follows an F distribution. If these two sample variances come from normally distributed populations, their ratio should also follow an F distribution, with numerator and denominator degrees of freedom one less than the sample sizes of the respective groups. If the p-value of the test statistic is less than the chosen significance level, the null hypothesis that the two population variances are equal is rejected.