Nonpooled t-test: both normal and unequal population standard deviations (thus not the same shape)
Mann-Whitney: same shape but not normal.
Thus it is best to use the Mann-Whitney test (and it is also resistant to outliers).
In there a relationship between confidence intervals and two-tailed hypothesis tests? The answer is yes. Let c be the level of confidence used to construct a confidence interval from sample data. Let * be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean: For a two-tailed hypothesis test with level of significance a and null hypothesis \(H_0 : mu = k\) we reject Ho whenever k falls outside the \(c = 1 — \alpha\) confidence interval for mu based on the sample data. When A falls within the \(c = 1 — \alpha\) confidence interval. we do reject \(H_0\). For a one-tailed hypothesis test with level of significance Ho : mu = k and null hypothesiswe reject Ho whenever A falls outsidethe \(c = 1 — 2\alpha\) confidence interval for p based on the sample data. When A falls within the \(c = 1 — 2\alpha\) confidence interval, we do not reject \(H_0\). A corresponding relationship between confidence intervals and two-tailed hypothesis tests is also valid for other parameters, such as \(p,\mu_1 — \mu_2,\) and \(p_1, - p_2\). (b) Consider the hypotheses \(H_0 : p_1 — p_2 = O\) and \(H_1 : p_1 — p_2 =\) Suppose a 98% confidence interval for \(p_1 — p_2\) contains only positive numbers. Should you reject the null hypothesis when alpha = 0.05? Why or why not?