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 18-year-olds are eligible for military service?” He asks listeners to go to his website and vote “Yes” if they agree the drinking age should be lowered and “No” if not. Of the 100 people who voted, 70 answered “Yes.” Which of the following conditions are violated?

I. Random

II. 10%

III. Large Counts

a. I only

b. II only

c. III only

d. I and II only

e. I, II, and III

Short answer

The required correct option is$\left(a\right)$

Step-by-step solution

Given information

$$\begin{gathered} n=100 \\ x=70 \end{gathered}$$

The objective is to explain which of the conditions for calculating a confidence interval for the population proportion.

Because they were not chosen at random, the condition of random selection is not satisfied. They simply took an answer from people. As a result, the random sample condition is not met.

The sample size should be less than $10\%$of the total population. In this case, $100$represents less than $10\%$of the large audience set. As a result, this condition was satisfied.

The final condition is that the number of successes and failures must be$\ge 10$. As a result, the number of successes is $70$and number failures

$=100-70\ge 10$that is met.

Hence, this condition is met.

Therefore, Only condition of random is not satisfied.