Question

A study of the career paths of hotel general managers sent questionnaires to an SRS of 280 hotels belonging to major U.S. hotel chains. There were 168 responses. The average time these 168 general managers had spent with their current company was 9.98 years. Take it as known that the standard deviation of time with the company for all general managers is 2.2 years. Give your answers to at least 2 decimal places, and use at least 3 decimal places in your critical value. (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: equation editorEquation Editor 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: equation editorEquation Editor years (c) In general, increasing the confidence level Increases equation editorEquation Editor the margin of error (width) of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT CHANGE'' or ''INCREASES'', without the quotes.)

Answer 1

Answer)

As the population standard deviation is known here (2.2), so we can use standard normal z table to estimate the answers

Sample size is 168

That is n = 168

Margin of error is given by critical value z *(s.d/√n)

A)

From z table, critical value z for 80% confidence interval is 1.28

So, margin of error = 1.28*(2.2/√168)

MOE = 0.2172591167466 = 0.22

B)

Critical value z from z table for 99% confidence level is 2.576

MOE = 2.576*(2.2/√168)

= 0.4372339724525

= 0.44

C)

As the confidence level increases, margin of error also increases

As MOE IS directly proportional to confidence level