Recently. the Shine research clinic published a report stating that the regular application of a very popular sunscreen lotion ContraHelios might cause some forms of skin cancer. The manufacturer of ContraHelios issued an energetic counterstatement asserting that the Shine clinic's conclusions were statistically inconsistent. Take Care pharmacy chain has been selling ContraHelios lotion for a long time. The market research department of Take Care wants to see what is currently happening with ContraHelios lotion demand. The members of a random sample of customers were asked about their willingness to use ContraHelios before and after the publication of Shine clinic's report. The answers were provided in form of a score from 0 to 10 (higher score means more willingness}. Results for five customers are shown in the following table. The "before" score is matched to the "after" score, and the difference should be calculated. Suppose that it is known that such differences have approximately bell-shaped distribution. Part I. Suppose that differences are d : Before After . Find the sample mean at and sample standard deviation ad of the differences. Step 1. Fill in the column \"d = Before After " of the table. Then, calculate if and fill in the cell below the table. Step 2. Using (1 , fill in the last two columns of the table. Participant Before After DEBUG? DDDDDD\" [:1 :1 l:l Total D Sample mean of the differences is d = Please, round your answer to 2 decimal places. Standard deviation of the differences is 3d = C] Part II. At a 3% significance level test the claim that the publications of clinic's report reduced,on average, the willingness to use ContraHelios lotion. Hint: Use the Student t distribution test for matched pairs and the following formula .3 () (a) State the null and alternative hypotheses, and identify which one is the claim. Which one is the claim? t\": 0H1 OHD For parts lb), (c) use the correct sign for the critical value (s) and test statistic, and round your answers to 3 decimal places. (b) Identify the test type and find the critical valuels). The test is Please select the correct sign for the critical value(s) and round your answers to 3 decimal places. Critical value (5} = C] (c) What is the test statistic? You do not need to enter the sign of the test statistic in the separate box. Put minus sign if the value is negative and put no sign if the value is positive. Round your answers to 2 decimal places. tst = (d) Is the null hypothesis rejected? Is the alternative hypothesis supported? O Fail to reject Ho (claim) and support H1 O Reject Ho (claim) and fail to support H1 O Fail to reject Ho and fail to support H1 (claim) O Reject Ho and support H1 (claim) (e) Select the correct conclusion. At a 3% level of significance, there is not sufficient sample evidence that the scores, on average, become lower after publications. O There is no difference in scores before and after publications. The scores, on average, become higher after publications. O At a 3% level of significance, the sample data support the claim that the scores, on average, become lower after publications