Question

A study of the career paths of hotel general managers sent questionnaires to an SRS of 230 hotels belonging to major U.S. hotel chains. There were 119 responses. The average time these 119 general managers had spent with their current company was 11.63 years. (Take it as known that the standard deviation of time with the company for all general managers is 1.3 years.)

Find the margin of error for a 90% confidence interval to estimate the mean time a general manager had spent with their current company.

Answer 1

The value is
`E = 0.196`

Explanation:

From the question we are told that

The sample size is n = 119

The sample mean is
`\= x = 11.63 \ years`

The standard deviation is
`s = 1. 3 \ years`

Given that the confidence level is 90% then the level of significance is mathematically represented as

`\alpha = (100 - 90) \%`

=>
`\alpha = 0.10`

The critical value of
`(\alpha )/(2)` obtained from the normal distribution table is

`Z_{(\alpha )/(2) } = 1.645`

Generally th margin of error is mathematically represented as

`E = Z_{(\alpha )/(2) } * (s)/(√(n) )`

=>
`E = 1.645* (1.3)/(√(119) )`

=>
`E = 0.196`