For each problem, select the best response.

(a) A radio talk show host with a large audience is interested in the proportion $p$ of adults in his listening area who think the drinking age should be lowered to 18. He asks, 'Do you think the drinking age should be reduced to 18 in light of the fact that 18 year olds are eligible for military service?' He asks listeners to phone in and vote 'yes' if they agree the drinking age should be lowered to 18, and 'no' if not. Of the 100 people who phoned in, 70 answered 'yes.' Which of the following assumptions for inference about a proportion using a confidence interval are violated?

A. The sample size is large enough so that the count of successes $n\hat{p}$ is 15 or more.
B. The data are an SRS from the population of interest.
C. The sample size is large enough so that the count of failures $n(1-\hat{p})$ is 15 or more.
D. The population is at least ten times as large as the sample.

(b) A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of 1200 registered voters and found that 620 would vote for the Republican candidate. Let $p$ represent the proportion of registered voters in the state who would vote for the Republican candidate. How large a sample $n$ would you need to estimate $p$ with a margin of error 0.01 with 95 percent confidence? Use the guess $p = .5$ as the value of $p$.

A. 4800
B. 49
C. 1500
D. 9604

(c) A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of 1200 registered voters and found that 620 would vote for the Republican candidate. Let $p$ represent the proportion of registered voters in the state who would vote for the Republican candidate. A 90 percent confidence interval for $p$ is:

A. 0.517 $\pm$ 0.014
B. 0.517 $\pm$ 0.249
C. 0.517 $\pm$ 0.028
D. 0.517 $\pm$ 0.024