Question

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 eighteen. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-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 and "No" if not. Of the $100$people who phoned in, $70$answered "Yes." Which of the following conditions for inference about a proportion using a confidence interval are violated?

I. The data are a random sample from the population of interest.

II. $n$is so large that both $n\overbrace{p}andn\left(1-\overbrace{p}\right)$are at least $10$.

III. The population is at least $10$times as large as the sample.

(a) I only

(c) III only

(c) I, II, and III

(b) II only

(d) I and II only

Short answer

(a) I only

Step-by-step solution

Step-1 Given Information

Given in the question that,

number of success $\left(X\right)=70$

number of trials$\left(n\right)=100$we have to find the correct option.

Step-2 Explanation

Here, sampling has been using the method of voluntary response sample and one of the conditions to create the confidence interval for population proportion is that the sample should be selected using the technique of simple random sampling. Thus, the condition of simple random sample is not met here.

Hence, the correct option is (a).