Q.9 - The Practice of Statistics for AP

Question

How confident? The figure below 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 $80\%$.

Step 1: Given Information

The result of $25$ SRSs:

Step 2: Explanation

The red lines under the curve represent the sample means that does not contain the true population mean $\mu$.

We note that there are $4$ out of the $25$ samples that do not contain the true proportion and thus $21$ out of the $25$ samples contain the true mean:

$\frac{21}{25}=0.84=84\%$

The nearest confidence level is $80\%$