Question 2
$0 / 1$ pt 100
Details
Suppose you compute a confidence interval with a sample size of 24 . What will happen to the confidence interval if the sample size increases to 46 ?
The confidence interval will widen.
The confidence interval will narrow.
The width of the confidence interval will stay the same.
Check Answer
Question 3
$0 / 1$ pt 100 (i) Detai

Step 1 ：The question is asking about the effect of increasing the sample size on the confidence interval. In statistics, a confidence interval is a range of values, derived from a data set, that is likely to contain the value of an unknown population parameter. The width of the confidence interval gives us an idea of how uncertain we are about the unknown parameter. A wider interval may indicate more uncertainty, and a narrower interval may indicate less uncertainty.

Step 2 ：When we increase the sample size, we are essentially collecting more data. More data tends to give us a better estimate of the population parameter, and thus, less uncertainty. Therefore, the confidence interval should narrow as the sample size increases.

Step 3 ：Let's confirm this with a simple simulation. We'll generate two samples, one with size 24 and the other with size 46. We'll then compute the 95% confidence intervals for the mean of the distribution from each sample. The mean of a sample is an estimate of the population mean, and the confidence interval gives us an idea of how accurate that estimate is.

Step 4 ：As we can see from the output, the confidence interval for the sample with size 24 is approximately (-0.04, 0.84), and the confidence interval for the sample with size 46 is approximately (-0.53, 0.06). The width of the confidence interval (which is the difference between the upper and lower bounds) is smaller for the sample with size 46 than for the sample with size 24. This confirms our initial thought that the confidence interval should narrow as the sample size increases.

Step 5 ：Final Answer: The confidence interval will \(\boxed{narrow}\).