Question

A recent report for a regional airline reported that the mean number of hours of flying time for its pilots is 63 hours per month. This mean was based on actual flying times for a sample of 45 pilots and the sample standard deviation was 7 hours. 2. Calculate a 90% confidence interval estimate of the population mean flying time for the pilots. Round your result to 4 decimal places. ( , ) 3.Using the information given, what is the smallest sample size necessary to estimate the mean flying time with a margin of error of 1.75 hour and 90% confidence? Note: For consistency's sake, round your t* value to 3 decimal places before calculating the necessary sample size.

Answer 1

t critical value at 0.10 df with 44 df = 1.680

90% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

63 - 1.680 * 7 / sqrt(45) < < 63 + 1.680 * 7 / sqrt(45)

61.247 < < 64.753

90% CI is ( 61.247 , 64.753 )

Sample size = (t * S / E)²

= ( 1.680 * 7 / 1.75)²

= 45.15

Sample size = 46 (Rounded up to nearest integer)