A study was conducted to investigate the effectiveness of acupuncture in reducing depression. Results for randomly selected subjects are shown in the following table. A lower score indicates less depression. The "before" value is matched to the "after" value, 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 d and the 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. Patient Before After d d - d (d - d 2 7 7 5 2 2 3 3 5 3 4 10 5 5 5 6 5 3 8 6 8 7 TotalSample mean of the differences is a? = [ 1 Please, round your answer to 2 decimal places. Standard deviation of the differences is sd = [ ] Part II. A researcher claims that the scores, on average, become lower after acupuncture. Test the researcher's claim at a 1% signicance level. Hint: Use the Student t distribution test for matched pairs and the following formula [a] State the null and alternative hypotheses, and identify which one is the claim. HI}: Select an answer B ?_B [ 1 H1: Select an answer B ?_B [ ] Which one is the claim? .-. H1 .-. HI} For parts (hi, to} use the correct sign for the critical value {s} and test statistic, and round your answers to 3 decimal places. {b} Identifyr the test type and find the critical valuels}. The test is Select an answer B Please select the correct sign for the critical value(s) and round your answers to 3 decimal places. Critical value (s) = 1 0 (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? Fail to reject Ho (claim) and support H1 Reject Ho and support H1 (claim) Fail to reject Ho and fail to support H1 (claim) Reject Ho (claim) and fail to support H1 (e) Select the correct conclusion. O At a 1% level of significance, there is not sufficient sample evidence that the scores, on average, become lower after acupuncture. o The scores, on average, become higher after acupuncture. There is no difference in scores before and after acupuncture. O At a 1% level of significance, the sample data support the claim that the scores, on average, become lower after acupuncture