Question

Consider the following situation . . .

Matilda has constructed three confidence intervals, all from the same random sample. The confidence levels are 95%, 98%, and 99.9%. The confidence intervals are 6.4 < μ < 12.3, 5.1 < μ < 13.6, and 6.8 < μ < 11.9. Unfortunately, Matilda has forgotten which confidence interval goes with which level. Match each confidence interval with its level.

Write a post for the discussion board that indicates which confidence interval goes with each of the confidence levels. (You may refer to the confidence intervals using interval notation such as (6.4, 12.3) rather than inequality notation as expressed above.) Also, indicate whether these confidence intervals are for a population mean or for a population proportion. Please include support with your results.

Answer 1

As we increase the confidence level, the width of confidence interval increases. Hence,

95% confidence interval will be having lowest width, followed by 98% confidence interval and the maximum width would be of 99.9% confidence interval. So,

95% confidence interval: 6.8 < μ < 11.9

98% confidence interval: 6.4 < μ < 12.3

99.9% confidence interval: 5.1 < μ < 13.6

These confidence intervals are for population mean because limits for population proportion would be between 0 and 1.