Question

A fitness center is interested in finding a 98% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 257 members were looked at and their mean number of visits per week was 3.2 and the standard deviation was 1.8. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a distribution.

b. With 98% confidence the population mean number of visits per week is between and visits.

c. If many groups of 257 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per week and about percent will not contain the true population mean number of visits per week.

Answer 1

a.

We use T-distribution here because the population standard deviation is not known to us.

b.

With 98% confidence the population mean number of visits per week is between 2.937 and 3.463 visits.

c.

About 98% percent of these confidence intervals will contain the true population mean number of visits per week and about 2% percent will not contain the true population mean number of visits per week.