Question

A researcher wants to determine a 99% confidence interval for the mean number of hours that adults spend per week doing community service. How large a sample should the researcher select so that the estimate is within 1.4 hours of the population mean? Assume that the standard deviation for time spent per week doing community service by all adults is 3 hours.

Answer 1

Here confidence interval = 99%

standard deviation of the population mean = $\sigma$ = 3 hrs

margin of error = critical test statistic * standard errro of sample mean

margin of error = 1.4 hours

critical test statistic for 99% confidence interval = 2.576

standard error of sample mean = 3/$\sqrt n$

1,4 = 2.576 * 3/$\sqrt n$

$\sqrt n$ = (2.576 * 3)/1.4

n = 30.47 or 31