Question

Dan, an office manager, wants to replace the catering company in charge of the office lunch. the new company promises the same quality of food at a smaller cost. before he makes the switch between companies, dan sends out a satisfaction survey of the old company to a sample of 30 3030 employees. after a month with the new company, he sends out the same satisfaction survey to the same group of employees. each survey produces a satisfaction rating. dan wants to test if the results suggest a significant difference in the average satisfaction rating between the old and the new catering companies. assume that the necessary conditions for inference were met. which of these is the most appropriate test and alternative hypothesis?

Paired t test with H : difference > 0 Paired t test with H.: Adifference #0 Two-sample t test with H : Company A > Company B Two-sample t test with H. : Company A+ Company B Two-sample t test with H: Company A Company B

Answer 1

A paired t-test is used because the same employees are surveyed before and after the switch, and their scores are compared. The alternative hypothesis should be that there is a significant difference in satisfaction levels, represented as 'difference ≠ 0', for a two-tailed test.

Step-by-step explanation:

In this case, a paired t-test is the most appropriate analysis method because Dan is comparing satisfaction scores from the same group of employees before and after switching catering companies. The test will look at the differences in each pair of scores (pre-change and post-change for the same individual).

For the alternative hypothesis (Ha), if Dan wishes to demonstrate a significant difference in satisfaction levels but not in a specific direction, he should use a two-tailed test, which is represented by Ha: difference ≠ 0. This states that there is a significant difference, either higher or lower, between the old and new company's satisfaction ratings.

Answer 2

The most appropriate test for comparing satisfaction ratings of the same group of employees before and after switching catering services is a paired t-test, with the alternative hypothesis stating that there is a significant difference in satisfaction ratings.

Step-by-step explanation:

Hypothesis Testing for Matched or Paired Samples

Since Dan sent out the same satisfaction survey to the same group of employees before and after switching the catering company, the most appropriate test for this scenario is a paired t-test (also known as a matched pairs t-test). A paired t-test is used when you have two sets of related observations, like the same group of employees rating two different catering companies.

The null hypothesis, in this case, would typically state there is no difference in the satisfaction ratings, while the alternative hypothesis would be that there is a significant difference. Because Dan is interested in whether there is any change (not necessarily if one is better than the other), the alternative hypothesis (Ha) should be non-directional, which is stated as there being a nonzero difference in satisfaction ratings. Thus, the correct hypothesis and test choice would be: Paired t-test with Ha: difference ≠ 0.