Question

a.

How well do the 95% confidence intervals do at capturing the true population mean when

samples sizes are small?

b. Does a larger sample size mean that the intervals are more likely to capture the true population value? Why? Note THIS is an

important concept and relates back to the Sampling Distribution of Sample Means.

Answer 1

a. How well do the 95% confidence intervals do at capturing the true population mean when sample sizes are small?

When the sample size is small, the width of confidence interval increases due to a decrease in the sampling error and a large amount of data is collected in the confidence interval. This means that the 95% confidence intervals are more likely of capturing the true population mean when sample sizes are small.

b. Does a larger sample size mean that the intervals are more likely to capture the true population value? Why?

Please note that with the increase in sample size, the width of the confidence interval decreases due to an increase in the sampling error. This means that the 95% confidence intervals are less likely of capturing the true population mean when sample sizes are large.