Question

Use the SEM formula and show all work.

How satisfied are hotel managers with the computer systems their hotels use? A survey was sent to 400 managers in hotels of size 200 to 500 rooms in Chicago and Detroit. In all, 101 managers returned the survey. Two questions concerned their degree of satisfaction with the ease of use of their computer systems and with the level computer training they had received. The managers responded using a seven-point scale, with 1 meaning "not satisfied", and 4 meaning "moderately satisfied," and 7 meaning "very satisfied".

a. What do you think is the population for this study? What are the major shortcomings in the obtained data?

b. The mean response for satisfaction with ease of use was 5.396. Find the 95% confidence interval for the managers sampled. (Assume the sample SD = 1.75)

c. Provide an interpretation for your answer in part B.

d. For satisfaction with training, the mean response was 4.398. Assuming the sample SD is 1.75, find the 99% confidence interval for the managers sampled.

e. Provide an interpretation of your answer obtained for part D.

Answer 1

a)

Population: Hotel managers in Chicago and Detroit.

Shortcomings: Sampling error (Non-response bias)

Explanation: The samples represent the population of hotel managers in Chicago and Detroit. Since some hotel managers failed to respond, the non-response bias occurs in the sampling such that fewer participants in the study which results in a higher variance in the parameter estimate.

b)

95% confidence interval = (5.0505, 5.7415

Explanation: The confidence interval is obtained using the following formula,

where

The t critical value is obtained from the t distribution table for significance level = 0.05, degree of freedom = n-11=100 and for two-tailed distribution,

Now,

c)

We are 95% confident that the mean response for the satisfaction with ease of use of hotel managers lies in the range from 5.0505 to 5.7415.

d)

95% confidence interval = (3.9407,4.8553)

Explanation: The confidence interval is obtained using the following formula,

where

The t critical value is obtained from the t distribution table for significance level = 0.01, degree of freedom = n-11=100 and for two-tailed distribution,

Now,

e)

We are 99% confident that the mean response for the satisfaction with the training of hotel managers lies in the range from 3.9407 to 4.8553.