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 meand-and sample standard deviation sdsd of the differences.

Step 1.Fill in the column "d=BeforeAfter " of the table. Then, calculatedand fill in the cell below the table.

Step 2. Usingd-, fill in the last two columns of the table.

Consumer	Before	After	d	dd	(dd)2
1	160	154
2	147	143
3	136	132
4	126	123
5	144	143
6	129	129
Total

Sample mean of the differences isd=

Please, round your answer to 2 decimal places. Standard deviation of the differences is sd=

Part II.Test the company's claim at a 1.5% significance level.

Hint:Use the Studenttdistribution test for matched pairs and the following formula

tst=dd(sdn)

(a) State the null and alternative hypotheses, and identify which one is the claim.

(a) State the null and alternative hypotheses, and identify which one is the claim. H0H0: Select an answer: d s p x choose one: < = > ans:____ H1H1: Select an answer: s x p d choose one: < = > ans:____ Which one is the claim?

• H0
• H1

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 and find the critical value(s).

The test is Select an answer: 1. two-tailed 2. right-tailed 3. left-tailed

Please select the correct sign for the critical value(s) and round your answers to 3 decimal places.

Critical value (s) =choose one: + ans____

(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.

tst=

(d) Is the null hypothesis rejected? Is the alternative hypothesis supported?

• Fail to rejectH0H0(claim) and supportH1H1
• RejectH0H0and supportH1H1(claim)
• Fail to rejectH0H0and fail to supportH1H1(claim)
• RejectH0H0(claim) and fail to supportH1H1

(e) Select the correct conclusion.

• We prove that, on average, there is no difference in systolic blood pressure values before and after taking the new medication.
• At a 1.5% level of significance, the sample data support the claim that that, on average, the new product lowers blood pressure
• At a 1.5% level of significance, there is not sufficient sample evidence that, on average, the new product lowers blood pressure
• We prove that the new medication elevates systolic blood pressure, on average.