Question: In order to cut costs a wine producer is considering using duo or 1 + 1 corks in place of full natural wood corks, but is concerned that it could affect buyers's perception of the quality of the wine. The wine producer shipped eight pairs of bottles of its best young wines to eight wine experts. Each pair includes one bottle with a natural wood cork and one with a duo cork. The experts are asked to rate the wines on a one to ten scale, higher numbers corresponding to higher quality. The results are:
a. Give a point estimate for the difference between the mean ratings of the wine when bottled are sealed with different kinds of corks.
b. Construct the 90% confidence interval based on these data for the difference.
c. Test, at the 10% level of significance, the hypothesis that on the average duo corks decrease the rating of the wine.