Question 5
Recently, the All about Skin 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 All about Skin clinic's conclusions were statistically inconsistent. Be Healthy pharmacy chain has been selling ContraHelios lotion for a long time. The market research department of Be Healthy 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 All about Skin 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 1. Suppose that differences are d = Before - After . Find the sample mean d and sample standard deviation sa of the differences. Step 1. Fill in the column "d = Before - After " of the table. Then, calculate d and fill in the cell below the table. Step 2. Using d , fill in the last two columns of the table. Participant Before After d (a - 2 ) 4 W 4 2 2 0 5 6 Total Sample mean of the differences is d = Please, round your answer to 2 decimal places. Standard deviation of the differences is 8 = 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.Sample mean of the differences is d Please, round your answer to 2 decimal places. Standard deviation of the differences is sa = 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 Ha (a) State the null and alternative hypotheses, and identify which one is the claim. Ho: Select an answer |? H1: Select an answer . ? c Which one is the claim? OHo OH1 For parts (b), (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 value(s). The test is Select an answer Please select the correct sign for the critical value(s) and round your answers to 3 decimal places. Critical value (s) - ? (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.(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. tat (d) Is the null hypothesis rejected? Is the alternative hypothesis supported? Reject Ho and support H1 (claim) Fail to reject Ho (claim) and support H1 Fail to reject Ho and fail to support H1 (claim) O Reject Ho (claim) and fail to support H1 (e) Select the correct conclusion. At a 3% level of significance, the sample data support the claim that the scores, on average, become lower after publications. There is no difference in scores before and after publications. The scores, on average, become higher after publications. At a 3% level of significance, there is not sufficient sample evidence that the scores, on average, become lower after publications
