# Question

Repeat Exercise 8 with the additional assumption that σ1 = σ2. How are the results affected by this additional assumption?

Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal σ1 = σ2, so that the standard error of the differences between means is obtained by pooling the sample variances as described in Part 2 of this section.

Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Do the following:

a. Test the given claim using the P-value method or critical value method.

b. Construct a confidence interval suitable for testing the given claim.

Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal σ1 = σ2, so that the standard error of the differences between means is obtained by pooling the sample variances as described in Part 2 of this section.

Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Do the following:

a. Test the given claim using the P-value method or critical value method.

b. Construct a confidence interval suitable for testing the given claim.

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