A natural wellness and beauty company claims that, on average, their new product lowers blood pressure. A group of six consumers was randomly selected and their systolic blood pressure was measured before and one month after they started taking the supplement. Results are shown in the table below. 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 sample standard deviation #, 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. Consumer | Before After d d - d d - d ) 120 123 131 131 135 134 132 130 5 162 158 151 149 Total Sample mean of the differences is d Please, round your answer to 2 decimal places. Standard deviation of the differences is s = Part II. Test the company's claim at a 1.5% significance level. Hint: Use the Student t distribution test for matched pairs and the following formula d Pyl - (a) State the null and alternative hypotheses, and identify which one is the claim. Ho: Select an answer V ) ? v H1: Select an answer v ? v Which one is the claim? O Ho OH, 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 vo] Please select the correct sign for the critical value(s) and round your answers to 3 decimal places. Critical value (s) = [? v(c) What is the test statistic? You do not need to enter the sign of the test statistic in the separate box. Round your answers to 2 decimal places. tat = (d) Is the null hypothesis rejected? Is the alternative hypothesis supported? O Reject Ho (claim) and fail to support H, O Reject Ho and support H1 (claim) O Fail to reject Ho and fail to support Hi (claim) O Fail to reject Ho (claim) and support H1 (e) Select the correct conclusion. O We prove that, on average, there is no difference in systolic blood pressure values before and after taking the new medication. O At a 1.5% level of significance, there is not sufficient sample evidence that, on average, the new product lowers blood pressure O At a 1.5% level of significance, the sample data support the claim that that, on average, the new product lowers blood pressure O We prove that the new medication elevates systolic blood pressure, on average
