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 267 members were looked at and their mean number of visits per week was 3.3 and the standard deviation was 1.7. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a distribution. b. With 95% confidence the population mean number of visits per week is between and visits. c. If many groups of 267 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.
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To compute the confidence interval, we need to use the formula: CI = x̄ ± z*(σ/√n) where x̄ is the sample mean (3.3), σ is the population standard deviation (we don't know this, so we use the sample standard deviation of 1.7 as an estimate), n is the sample size Show more…
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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 234 members were looked at and their mean number of visits per week was 3.4 and the standard deviation was 1.8. Round answers to 3 decimal places where possible. A) To compute the confidence interval use a Z or T distribution? B) With 95% confidence the population mean number of visits per week is between ______ and _____ visits. C) If many groups of 234 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.
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