Question

10. Properties of a confidence interval Suppose the mean of a population is 22. A researcher (who does not know that p Then she constructs a 95% confidence interval of the population mean. 22) selects a random sample of size n from this population. The true population mean and the researcher's 95% confidence interval of the population mean are shown in the following graph. Use the graph to answer the questions that follow Sample Mean 95% Confidence interval of the population Mean True Population Mean 21 22 23 24 25 26 27 28 29 30 31

Answer 1

Lower Limit = 23

Upper limit = 30

Sample mean = (30-23)/2 = 3.5

In this case, t_SM = 3.5

Compared with the center of the 95% confidence interval, the center of the 85% confidence interval is same.

Compared to the 95% confidence interval, the 85% confidence interval is narrower.

At the same confidence level, increasing in the sample size would have a similar effect on the width of the confidence interval as changing the confidence level from 95% to 85%.