Question

Another response on the survey referred to in question 4 was the statement: “Response to concerns/complaints made during your stay”. The responses were 1 = very poor, 2 = poor, 3 = fair, 4 = good, and 5 = very good. The data from the survey respondents for the last month was analyzed. The respondents were stratified by whether or not they had a roommate. The following is computer output of an analysis of the mean responses for these for this statement between the group who did not have a roommate and the group who did have a roommate.

Two-Sample T-Test and Cl: 15, MATE Two-sample T for I5 StDev SE Mean No309 4.576 0.663 0.038 Yes 105 4.371 0.869 0.085 MATE N Mean Difference-mu (No) - mu (Yes) Estimate for difference: 0.2046 95% CI for difference: (0.0212, 0.3880)

What is the 95% confidence interval for the difference in the population mean responses for these two groups. Interpret this confidence interval. Did having a roommate impact how patients felt about how their concerns or complaints were handled?

Choose the best answer from the following:

i) The 95% confidence interval for the difference in means of the patients who did not have a roommate and the patients who did have a roommate is (0.0212, 0.3880). This implies that the mean for the patients who did not have a roommate could be the same as the mean of patients who did have a roommate. Thus the average evaluation regarding how their concerns of complaints were handled does not depend upon whether or not the patient had a roommate.
ii) The 95% confidence interval for the difference in means of the patients who did not have a roommate and the patients who did have a roommate is (0.0212, 0.3880). This implies that the mean for the patients who did not have a roommate is smaller than the mean of patients who did have a roommate. Thus patients who did not have a roommate had an average lower evaluation regarding how their concerns of complaints were handled than patients who did have a roommate.
iii) The 95% confidence interval for the difference in means of the patients who did not have a roommate and the patients who did have a roommate is (0.0212, 0.3880). This implies that the mean for the patients who did not have a roommate is larger than the mean of patients who did have a roommate. Thus patients who did not have a roommate had an average higher evaluation regarding how their concerns of complaints were handled than patients who did have a roommate.
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Answer #1

The best answer from the given options is Option i

The 95% CI for the difference in means is (0.0212, 0.3880).

This implies that 95% of unknown population parameters (difference in means), would lie between this interval.

This difference ranges from 0.0212 to 0.3880, which is marginal and not very signifcant.

Thus the means of the responses of the two groups is not very different implying the average evaluation regarding how their concerns of complaints were handled does not depend upon whether or not the patient had a roommate.

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