The paper “Does the Color of the Mug Influence the Taste of the Coffee?” (Flavour [2014]: 1–7) describes an experiment in which subjects were assigned at random to one of two treatment groups. The 12 people in one group were served coffee in a white mug and were asked to rate the quality of the coffee on a scale from 0 to 100. The 12 people in the second group were served the same coffee in a clear glass mug, and they also rated the coffee. The mean quality rating for the 12 people in the white mug group was 50.35 and the standard deviation was 20.17. The mean quality rating for the 12 people in the clear glass mug group was 61.48 and the standard deviation was 16.69. For this exercise, you may assume that the distribution of quality ratings for each of the two treatments is approximately normal.

a. Use the given information to construct and interpret a 95% confidence interval for the difference in mean quality rating for this coffee when served in a white mug and when served in a glass mug.

b. Based on the interval from Part (a), are you convinced that the color of the mug makes a difference in terms of mean quality rating? Explain.