Question

A fitness center is interested in finding a 95% 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 245 members were looked at and their mean number of visits per week was 2.4 and the standard deviation was 1.6. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? t z  distribution.

b. With 95% confidence the population mean number of visits per week is between ? and ? visits.

c. If many groups of 245 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 will use a z distribution since n > 30
b)

z @ 95.0% = 1.96

Required confidence interval = (2.4-0.2004, 2.4+0.2004)
Required confidence interval = (2.1996, 2.6004)
c) If many groups of 245 randomly selected members are studied, then a different confidence interval would be produced from each group. About 95 percent of these confidence intervals will contain the true population mean number of visits per week and about 5 percent will not contain the true population mean number of visits per week.
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