(b) Press the "Generate Samples" button below to simulate taking 19 more samples of size \( n=12 \) from the population. Notice that the confidence intervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table.
(c) Notice that for \( \frac{18}{20}=90 \% \) of the samples, the \( 95 \% \) confidence interval contains the population mean.
Choose the correct statement.
When constructing \( 95 \% \) confidence intervals for 20 samples of the same size from the population, exactly \( 95 \% \) of the samples will contain the population mean.
When constructing \( 95 \% \) confidence intervals for 20 samples of the same size from the population, at most \( 95 \% \) of the samples will contain the population mean.
When constructing \( 95 \% \) confidence intervals for 20 samples of the same size from the population, it is possible that more or fewer than \( 95 \% \) of the samples will contain the populion mean.
(d) Choose ALL that are true.
If there were a Sample 21 of size \( n=24 \) taken from the same population as Sample 15, then the \( 95 \% \) confidence interval for Sample 21 would be narrower than the \( 95 \% \) confidence interval for Sample 15.
The \( 80 \% \) confidence interval for Sar