A study of the career paths of hotel general managers sent questionnaires to an

Question

A study of the career paths of hotel general managers sent questionnaires to an SRS of 270 hotels belonging to major U.S. hotel chains. There were 165 responses. The average time these 165 general managers had spent with their current company was 11.03 years. (Take t as known that the standard deviation of time with the company for al general managers is 22 years) (a) Find the margin of error for a 90% 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 (c) In general, increasing the confidence level increases the margin of error (width) of the confidence interval.

Explanation / Answer

(a) Margin of error =  Critical value x Standard error of the statistic

Here confidence interval 90% so test statistic = 1.645

mean xbar= 11.03 years and standard deviation s = 2.2years

so standard error of the mean = s/n = 2.2/ 165 = 0.1713

so margin or error = 1.645 * 0.1713 = 0.2818 years.

(ii)

Margin of error =  Critical value x Standard error of the statistic

Here confidence interval 99% so test statistic = 2.575

mean xbar= 11.03 years and standard deviation s = 2.2years

so standard error of the mean = s/n = 2.2/ 165 = 0.1713

so margin or error = 2.575 * 0.1713 = 0.4411 years.

(c) in General, increase in confidence interval will increase the margin of error.

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