Question

Select the most appropriate response.

As sample size decreases (other things being equal), what tends to happen to 95% confidence intervals?

Answer 1

When the sample size decreases, the 95% confidence interval becomes wider to account for the increased variability in the data.

Step-by-step explanation:

When the sample size decreases, the 95% confidence interval tends to become wider. This is because with a smaller sample size, there is more uncertainty and variability in the data. As a result, the confidence interval needs to be wider in order to capture the true population parameter with a certain level of confidence.

For example, let's say we have two samples: Sample A with 100 observations and Sample B with 50 observations. If we calculate the 95% confidence intervals for both samples, we would expect the interval for Sample B to be wider than the interval for Sample A.

Therefore, as the sample size decreases, the 95% confidence interval becomes wider to account for the increased variability in the data.