Recently, the Shine research clinic published a report stating that the regular application of a very popular sunscreen lotion NoHelios might cause some forms of skin cancer. The manufacturer of NoHelios issued an energetic counterstatement asserting that the Shine clinic's conclusions were statistically inconsistent. Wellbeing pharmacy chain has been selling NoHelios lotion for a long time. The market research department of Wellbeing wants to see what is currently happening with NoHelios lotion demand. The members of a random sample of customers were asked about their willingness to use NoHelios before and after the publication of Shine 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 I. Suppose that differences are d=d= Before−-After . Find the sample mean −dd -and sample standard deviation sdsd of the differences. Step 1. Fill in the column "d=d= Before−-After " of the table. Then, calculate −dd - and fill in the cell below the table. Step 2. Using −dd - , fill in the last two columns of the table. Participant Before After dd d− −dd-d - (d− −d)2(d-d -)2 1 -1 0 2 5 3 3 6 3 4 4 6 5 7 4 Total Sample mean of the differences is −d=d -= Please, round your answer to 2 decimal places. Standard deviation of the differences is sd=sd= Part II. At a 1% significance level test the claim that the publications of clinic's report reduced,on average, the willingness to use NoHelios lotion. Hint: Use the Student t distribution test for matched pairs and the following formula tst= −d−μd(sd√n)tst=d --μd(sdn) (a) State the null and alternative hypotheses, and identify which one is the claim. H0H0: H1H1: Which one is the claim? H1H1 H0H0 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. 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=tst= (d) Is the null hypothesis rejected? Is the alternative hypothesis supported? Reject H0H0 (claim) and fail to support H1H1 Fail to reject H0H0 (claim) and support H1H1 Fail to reject H0H0 and fail to support H1H1 (claim) Reject H0H0 and support H1H1 (claim) (e) Select the correct conclusion. At a 1% level of significance, the sample data support the claim that the scores, on average, become lower after publications. At a 1% level of significance, there is not sufficient sample evidence that the scores, on average, become lower after publications. The scores, on average, become higher after publications. There is no difference in scores before and after publications.
Recently, the Shine research clinic published a report stating that the regular application of a very popular sunscreen lotion NoHelios might cause some forms of skin cancer. The manufacturer of NoHelios issued an energetic counterstatement asserting that the Shine clinic's conclusions were statistically inconsistent.
Wellbeing pharmacy chain has been selling NoHelios lotion for a long time. The market research department of Wellbeing wants to see what is currently happening with NoHelios lotion demand. The members of a random sample of customers were asked about their willingness to use NoHelios before and after the publication of Shine 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 I. Suppose that differences are d=d= Before−-After . Find the sample mean −dd -and sample standard deviation sdsd of the differences.
Step 1. Fill in the column "d=d= Before−-After " of the table. Then, calculate −dd - and fill in the cell below the table.
Step 2. Using −dd - , fill in the last two columns of the table.
| Participant | Before | After | dd | d− −dd-d - | (d− −d)2(d-d -)2 |
| 1 | -1 | 0 | |||
| 2 | 5 | 3 | |||
| 3 | 6 | 3 | |||
| 4 | 4 | 6 | |||
| 5 | 7 | 4 | |||
| Total |
Sample mean of the differences is −d=d -=
Please, round your answer to 2 decimal places.
Standard deviation of the differences is sd=sd=
Part II. At a 1% significance level test the claim that the publications of clinic's report reduced,on average, the willingness to use NoHelios lotion.
Hint: Use the Student t distribution test for matched pairs and the following formula
tst= −d−μd(sd√n)tst=d --μd(sdn)
(a) State the null and alternative hypotheses, and identify which one is the claim.
H0H0:
H1H1:
Which one is the claim?
- H1H1
- H0H0
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. 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=tst=
(d) Is the null hypothesis rejected? Is the alternative hypothesis supported?
- Reject H0H0 (claim) and fail to support H1H1
- Fail to reject H0H0 (claim) and support H1H1
- Fail to reject H0H0 and fail to support H1H1 (claim)
- Reject H0H0 and support H1H1 (claim)
(e) Select the correct conclusion.
- At a 1% level of significance, the sample data support the claim that the scores, on average, become lower after publications.
- At a 1% level of significance, there is not sufficient sample evidence that the scores, on average, become lower after publications.
- The scores, on average, become higher after publications.
- There is no difference in scores before and after publications.
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