Question

Regarding the pooled and nonpooled t-procedures,

a. what is the difference in assumptions between the two procedures?

b. how important is the assumption of independent simple random samples for these procedures?

c. how important is the normality assumption for these procedures?

Short answer

Part (a)The assumptions for pooled t-test required equal population

Part (b)It is accurately required the assumption of independent simple random samples

Part (c)The distribution of the data is approximately normally distributed.

Step-by-step solution

Step 1:Given information

The pooled and nonpooled t-procedures,

Step 2:Part (a) Explaination

Difference in assumptions between pooled and nonpooled $t$-procedures:

Assumptionsfor pooled $t$-test:

- The selected sample should be a simple random sample from two populations.

- They are independent of one another.

- Population is approximately normal.

- Equal population standard deviations

Assumptions for nonpooled $t$-test:

- The selected sample should be a simple random sample from two populations.

- They are independent of one another.

- Population is approximately normal.

Therefore, it can be concluded that the assumptions for pooled t-test required equal population standard deviation but the assumptions for nonpooled t-test does not required.

Step 2:Part (b) Explaination

It is accurately required the assumption of independent simple random samples for pooled and nonpooled t-test procedure.

Step 2:Part (c) Explaination

For small sample, the normality assumption is more important for both pooled and nonpooled t-test procedure.

But for large samples, the normality assumption is less important because the central limit theorem is applied for large samples.

This tells us that the distribution of the data is approximately normally distributed.