The observations below resulted from independent random samples selected from approximate normal populations:
Sample 1: 4.5, 7.0, 3.1, 6.2, 5.8, 6.1
Sample 2: 6.5, 5.4, 7.8, 8.1, 7.9
a) Conduct a test of hypothesis to determine if the mean of the second population is greater than the mean of the first population. Assume that the population variances are equal. Use a .05 significance level.
b) Perform the statistical test in part a) but do not assume that the population variances are equal.