Chapter 8.2, Problem 34E

a)

To determine

To explain necessity of the conditions.

Answer to Problem 34E

The sampling distribution of the sample proportion is approximately Normal.

Explanation of Solution

Given:

When constructing a confidence interval for a population proportion, we check that both $n\widehat{p}andn(1-\widehat{p})\ge 10$ .

The condition of large count is, $n\widehat{p}andn(1-\widehat{p})$ both should be at least 10. Because we need that the large counts condition is satisfied such that we know that the sampling distribution of the sample proportion is approximately Normal.

If the large counts distribution is not satisfied, then the sampling distribution of the sample proportion will be skewed and thus we won't be able to use the Normal distribution to estimate the confidence interval.

b)

To determine

To explain what happen if the condition $n\widehat{p}andn(1-\widehat{p})\ge 10$ violet.

Answer to Problem 34E

There would be less chance to capture correct population parameter.

Explanation of Solution

Given:

When constructing a confidence interval for a population proportion, we check that both $n\widehat{p}andn(1-\widehat{p})\ge 10$ .

The condition of large count is, $n\widehat{p}andn(1-\widehat{p})$ both should be at least 10. Because we need that the large counts condition is satisfied such that we know that the sampling distribution of the sample proportion is approximately Normal.

If the large counts distribution is not satisfied, then the sampling distribution of the sample proportion will be skewed and thus we won't be able to use the Normal distribution to estimate the confidence interval. Therefore, there will not be possible to capture required/correct population parameter.