# Assume that you have a sample of n1 = 8 with the sample mean X_bar1 = 42 and a sample standard deviation of S1 = 4

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Assume that you have a sample of n1 = 8, with the sample mean X_bar1 = 42, and a sample standard deviation of S1 = 4, and you have an independent sample of n2 = 15 from another population with a sample mean of X_bar = 34 and a sample standard deviation of S2 = 5. What assumptions about the two populations are necessary in order to perform the pooled-variance t test for the hypothesis and make a statistical decision?

A. It is necessary to assume that the populations from which you are sampling have equal population means and positive standard deviations.
B. It is necessary to assume that the populations from which you are sampling have independent normal distributions and equal variances.
C. It is necessary to assume that the populations from which you are sampling have negative stat test statistics and unequal sample means.
D. It is necessary to assume that the populations from which you are sampling have unequal variances and equal sizes. Before conducting independent sample t-test using pooled variances, it is important to assume that the population variances are equal.

Analysis to test for differences in mean using Minitab.

Two-Sample T-Test and CI

Sample   N   Mean  StDev  SE Mean
1       18  42.00   4.00     0.94
2       15  34.00   5.00      1.3

Difference = μ (1) - μ (2)
Estimate for difference:  8.00
95% CI for difference:  (4.71, 11.29)
T-Test of difference = 0 (vs ≠): T-Value = 5.00  P-Value = 0.000  DF = 26