Question

A study of the career paths of hotel general managers sent questionnaires to an SRS of 250 hotels belonging to major U.S. hotel chains. There were 129 responses. The average time these 129 general managers had spent with their current company was 10.33 years. (Take it as known that the standard deviation of time with the company for all general managers is 2.1 years.)

(a) Find the margin of error for an 85% confidence interval to estimate the mean time a general manager had spent with their current company: _____ years

(b) Find the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company: _____ years

Answer 1

Solution :

Given that,

a) Z/2 = Z0.075 = 1.44

Margin of error = E = Z/2 * ( /n)

= 1.44 * ( 2.1 /  129 )

= 0.27 years

b) Z/2 = Z0.005 = 2.576

Margin of error = E = Z/2 * ( /n)

= 2.576 * ( 2.1 /  129 )

= 0.48 years