Question

Each pair of graphs in Fig. $10.8$shows the distributions of a variable on two populations. Suppose that, in each case, you want to perform a small-sample hypothesis test based on independent simple random samples to compare the means of the two populations. In each case, decide whether the pooled $t$-test, non pooled $t$-test, or neither should be used. Explain your answers.

Short answer

Part $\left(a\right)$: Pooled $t$-test.

Part $\left(b\right)$: Non pooled $t$-test.

Part $\left(c\right)$: Neither.

Part$\left(d\right)$: Neither.

Step-by-step solution

Part a Step 1. Given information

Part a Step 2. Pooled t-test:

In this case, the two populations are same and the shape of the distributions are symmetric and identical. So, we use the pooled$t$-test in this case.

Part b Step 1. Non pooled t-test:

In this case, the two populations are not the same and the shape of the distributions are not symmetric and identical. So, we use the non pooled $t$-test in this case.

Part c Step 1. Neither:

In this case, the two populations are not symmetric. So, the normality assumption is violated. Hence, we cannot use the$t$-test.

Part d Step 1. Neither:

In this case, the one of the population is not symmetric. So, the normality assumption is violated. Hence, we cannot use the$t$-test.