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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: 鈥淒o 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?鈥� He asks listeners to go to his website and vote 鈥淵es鈥� if they agree the drinking age should be lowered and 鈥淣o鈥� if not. Of the 100 people who voted, 70 answered 鈥淵es.鈥� 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

Step by step solution

01

Given information

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

02

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$鈮�10$. As a result, the number of successes is $70$and number failures

$=100-70鈮�10$that is met.

Hence, this condition is met.

Therefore, Only condition of random is not satisfied.

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