Recently, the Derma#1 research clinic published a report stating that the regular application of a very popular sunscreen lotion NoTitan might cause some forms of skin cancer. The manufacturer of Nonth issued an energetic counterstatement asserting that the Derma#1 clinic's conclusions were statistically inconsistent. Wellbeing pharmacy chain has been selling NoTitan lotion for a long time. The market research department of Wellbeing wants to see what is currently happening with NoTitan lotion demand. The members of a random sample of customers were asked about their willingness to use NoTitan before and after the publication of Derma#1 clinic's report. The answers were provided in form of a score from O 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 2 Before After. Find the sample mean of and sample standard deviation 5d of the differences. Step 1. Fill in the column "d : Before 7 After " of the table. Then, calculate d and fill in the cell below the table. Step 2. Using of ,fill in the last two columns of the table. _ 2 Participant Before After d d_ a; (d d) 1 2 O 2 4 2 3 5 4 4 6 3 5 8 6 Total 3 : Sample mean of the differences is d = Please, round your answer to 2 decimal places. Standard deviation of the differences is sd = C] Part II. At a 1% significance level test the claim that the publications of Derma#i clinic's report reduced, on average, the willingness to use NoTitan lotion. Hint: Use the Student tdistribution test for matched pairs and the following formula 5 (a) (a) State the null and alternative hypotheses, and identify which one is the claim. tst : Ho_-[: IIIID Which one is the claim? 0 H1 0 H0 (b) Identify the test type and find the critical value(s). The test is Please select the correct sign for the critical value(s) and keep 3 decimal places in your answer. 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. (d) Is the null hypothesis rejected? Is the alternative hypothesis supported? 0 Reject H0 (claim) and fail to support H1 0 Fail to reject H0 (claim) and support H1 0 Fail to reject Ho and fail to support H1 (claim) (d) Is the null hypothesis rejected? Is the alternative hypothesis supported? 0 Reject H0 (claim) and fail to support H1 0 Fail to reject H0 (claim) and support H1 0 Fail to reject Hg and fail to support H1 (claim) 0 Reject H0 and support H1 (claim) (e) Select the correct conclusion. 0 We prove that the scores before and after publication are equivalent. 0 The scores become significantly higher after publication. 0 At a 1% level of significance, there is not sufficient sample evidence to support the claim that the scores, on average, become lower after publication. 0 At a 1% level of significance, the sample data support the claim that the scoresr on average, become lower after publication