Q.1.2 - The Practice of Statistics for AP

Question

In each of the following settings, check whether the conditions for calculating a confidence interval for the population proportion p are met.

1. An AP Statistics class at a large high school conducts a survey. They ask the first 100 students to arrive at school one morning whether or not they slept at least 8 hours the night before. Only 17 students say "Yes."

2. A quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. Of the bags selected, 3 had too much salt.

Step-by-Step Solution

Answer

No, the condition of normality is not satisfied.

Step 1: GIven Information

Number of success (x) $=3$

Number of trials (n) $=25$

Step 2: Explanation

One of the required conditions to construct the confidence interval for proportion is that $n\hat{p}>10$

Here,

$$\begin{gathered} 25(0.12)=3 \\ <10 \end{gathered}$$

Thus, the conditional normality is not satisfied here.