Please help me with questions 2, 5, and 6

Page 1 of 4 ZOOM 2. (20 points) A gardener sets up a flower stand in a busy business district and sells bouquets of assorted fresh flowers on weekdays. To find a more profitable pricing, she sells bouquets for 15 dollars each for ten days, then for 10 dollars each for five days. Her average daily profit for the two different prices are given below. n X S $15 10 171 26 $10 5 198 29 Assume that the variances of the price on these two days are equal . a. Construct the 90% confidence interval for the difference in the population means based on these data. b. Test, at the 10% level of significance, whether the data provide sufficient evidence to conclude the gardener's average daily profit will be higher if the bouquets are sold at $10 each.Page of4 O ZOOM + 3" You're incognito 5. (25 points) Eight golfers were asked to submit their latest scores on their favorite golf courses. These golfers were each given a set of newly designed clubs. After playing with the new clubs for a few months, the golfers were again asked to submit their latest scores on the same golf courses. The results are summarized below. Wl Own clubs 77 73 73 72 75 77 New clubs 72 73 75 70 73 75 a. Compute Ci and sd. b. Give a point estimate for m - uz = pd. c. Construct the 90% confidence interval for in - u2 = \"d from these data. d. Test, at the 1% level of significance, the hypothesis that on average golf scores are lower with the new clubs. Page 4 of 4 ZOOM + 6. (25 points) 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: Wine Expert Duo Cork Wood Cork 8.5 8.5 2 8.0 8.5 6.5 8.0 7.5 8.5 5 8.0 7.5 6 8.0 8.0 9.0 9.0 7.0 7.5 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