-please show all work thanks (1 point) A study of the career paths of hotel gene

Question

-please show all work thanks

(1 point) A study of the career paths of hotel general managers sent questionnaires to an SRS of 240 hotels belonging to major U.S. hotel chains. There were 127 responses. The average time these 127 general managers had spent with their current company was 9.44 years. (Take it as known that the standard deviation of time with the company for all general managers is 1.6 years.) (a) Find the margin of error for an 80% 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 the margin of error (width) of the confidence interval. (Enter: "DECREASES DOES NOT CHANGE'' or "INCREASES", without the quotes.)

Explanation / Answer

a) ME0.80=Z(sigma/sqrt n)=1.28(1.6/sqrt 127)=0.18 years.

b) ME0.99=2.58(1.6/qrt 127)=0.37 years.

c) Margin of error increases. As with increase in confidence level, interval widens and so margin of error.

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