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 differenceshould be calculated. Suppose that it is known that such differences have approximately bell-shaped distribution.

Part I.Suppose that differences ared=

BeforeAfter .Find the sample mean dand sample standard deviationsd

of the differences.

Step 1. Fill in the column "d=

BeforeAfter " 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 dd (dd)2 1 125 124 2 134 131 3 133 134 4 158 156 5 149 146 6 132 128 Total Sample mean of the differences is d=

Please, round your answer to 2 decimal places.

Standard deviation of the differences issd=

Part II. Test the company's claim at a 3.5% significance level.

Hint: Use the Student t distribution 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.

H0

:

H1:

Which one is the claim?

• 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 type and find the critical value(s).

The test is

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. Round your answers to 2 decimal places.

tst=

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

• Reject H0

(claim) and fail to support H1 (claim) and support H1 and support H1 and fail to support H1

• (claim)

(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.
• We prove that the new medication elevates systolic blood pressure, on average.
• At a 3.5% level of significance, the sample data support the claim that that, on average, the new product lowers blood pressure
• At a 3.5% level of significance, there is not sufficient sample evidence that, on average, the new product lowers blood pressure

Question Help

Question 2

:

• Message Message instructor

H0

Fail to reject H0

Reject H0

(claim)

Fail to reject H0