Q.10 - The Practice of Statistics for AP

Question

How confident? The figure at top right shows the result of taking $25$ SRSs from a Normal population and constructing a confidence interval for each sample. Which confidence level—$80\%, 90\%, 95\%$, or $99\%$—do you think was used? Explain.

Step-by-Step Solution

Answer

The nearest confidence level is $99\%$.

Step 1: Given Information

The result of taking $25$ SRSs:

Step 2: Explanation

The red lines under the curve represent the sample means that do not contain the true population proportion.

We note that there are $0$ out of the $25$ samples that do not contain the true proportion and thus $25$ out of the $25$ samples contain the true proportion:

$\frac{25}{25}=1=100\%$

The nearest confidence level is $99\%$ (although $95\%$ could also be a possible used confidence level).