Estimate the population mean by finding a 99% confidence interval given a sample of size 17, with a mean of 51.6 and a standard deviation of 6.7.

Question

Estimate the population mean by finding a 99% confidence interval given a sample of size 17, with a mean of 51.6 and a standard deviation of 6.7.

What is the 99% confidence interval to estimate the population mean? Enter the tri-linear inequality values accurate to one decimal place.

Answer 1

Remember the formula for the Confidence interval is sample mean ± t_α/2,df=n-1•st.dev./√n.

To find the critical value, use a t-table or calculator (inverse T distribution function): t_{.005, 16} = 2.921

Now simply plug in all the values.

51.6 ± 2.921•6.7/√17 = 51.6 ± 4.7 = (46.9, 56.3)

This means we can be 99% confident that the population mean is between 46.9 and 56.3.