Compared to situations where the population is either infinite or very large compared to the sample size, what effect will the finite population correction tend to have on a. the width of a confidence interval?

b. the required size of a sample?

In Exercise 9.65, suppose that (unknown to the dealers) the actual population proportion is really $0.35$. If they use their estimated value $(\pi \leq 0.15)$ in determining the sample size and then conduct the study, will their maximum likely error be greater than, equal to, or less than $0.02$ ? Why?

The Chevrolet dealers of a large county are conducting a study to determine the proportion of car owners in the county who are considering the purchase of a new car within the next year. If the population proportion is believed to be no more than $0.15$, how many owners must be included in a simple random sample if the dealers want to be $90 \%$ confident that the maximum likely error will be no more than $0.02$ ?

Suppose that Nabisco would like to determine, with $95 \%$ confidence and a maximum likely error of $0.03$, the proportion of first graders in Pennsylvania who had Nabisco's Spoon-Size Shredded Wheat for breakfast at least once last week. In determining the necessary size of a simple random sample for this purpose:

b. Do you think the population proportion could really be as high as $0.5$ ? If not, repeat part (a) using an estimated proportion that you think would be more likely to be true. What effect does your use of this estimate have on the sample size?

Suppose that Nabisco would like to determine, with $95 \%$ confidence and a maximum likely error of $0.03$, the proportion of first graders in Pennsylvania who had Nabisco's Spoon-Size Shredded Wheat for breakfast at least once last week. In determining the necessary size of a simple random sample for this purpose:

a. Use $0.5$ as your estimate of the population proportion.

A national political candidate has commissioned a study to determine the percentage of registered voters who intend to vote for him in the upcoming election. To have $95 \%$ confidence that the sample percentage will be within 3 percentage points of the actual population percentage, how large a simple random sample is required?