3. A new medication is being developed to treat severe morning sickness in pregnant women. The information below was generated from a small sample size (n = 6) and shows the number of times a woman with morning sickness vomited both before and after treatment. Set up and interpret the results of a sign test at the alpha equals .05 level to determine if there is a difference in symptoms before and after treatment.

Pregnant Woman

Before Treatment

After Treatment

Difference

Sign

1

8

3

2

4

7

3

6

5

4

8

10

5

11

10

6

8

2

A) We reject H₀ in favor of H₁, which states the median difference in the number of vomiting episodes in a day before and after treatment are not equal because 2 is greater than the critical value 0 for a sign test with a population of only 6 individuals.

B) We reject H₀ in favor of H₁, which states the median difference in the number of vomiting episodes in a day before and after treatment are not equal because 4 is greater than the critical value 0 for a sign test with a population of only 6 individuals.

C) We fail to reject H₀, which states the median difference in the number of vomiting episodes in a day before and after treatment are equal because 2 is greater than the critical value 0 for a sign test with a population of only 6 individuals.

D) We fail to reject H₀, which states the median difference in the number of vomiting episodes in a day before and after treatment are equal because 4 is greater than the critical value 0 for a sign test with a population of only 6 individuals.

4. A new medication is being developed to treat severe nausea and vomiting among chemotherapy patients. The information below was generated from a small sample size (n = 11) and shows the number of times a chemotherapy patient vomited both before and after treatment due to the side effects of chemotherapy. Set up and interpret the results of a sign test at the alpha equals .05 level to determine if there is a difference in symptoms before and after treatment.

Chemotherapy Patient

Before Treatment

After Treatment

Difference

Sign

1

9

3

2

12

5

3

14

7

4

9

4

5

8

2

6

11

3

7

15

7

8

12

8

9

7

8

10

9

5

11

8

7

A) We reject H₀ in favor of H₁, which states the median difference in the number of vomiting episodes in a day before and after treatment are not equal because 1 is less or equal to the critical value 1 for a sign test with a population of only 11 individuals.

B) We reject H₀ in favor of H₁, which states the median difference in the number of vomiting episodes in a day before and after treatment are not equal because 10 is greater or equal to the critical value 1 for a sign test with a population of only 11 individuals.

C) We fail to reject H₀, which states the median difference in the number of vomiting episodes in a day before and after treatment are equal because 1 is less or equal to critical value 1 for a sign test with a population of only 11 individuals.

D) We fail to reject H₀, which states the median difference in the number of vomiting episodes in a day before and after treatment are equal because 10 is greater or equal to the critical value 1 for a sign test with a population of only 11 individuals.

5. A researcher is conducting a study on the palliative care of patients at a specific facility to determine how their chronic pain symptoms change after entering the palliative care environment. This study is aimed at determining the effectiveness of a standardized treatment protocol for the patients entering into the palliative care environment. To do this, the researcher is comparing the pain scores of individuals before treatment and after treatment. Set up a Wilcoxon signed-ranks test and interpret it at the alpha equals .05 level.

Patient

Before Treatment

After Treatment

Value of Differences

Ordered Absolute Values of Differences

Ranks

Sign Rank

1

9

4

5

2

10

5

5

3

7

3

4

4

8

5

3

5

6

7

-1

6

9

5

4

7

6

4

2

8

7

3

4

9

9

4

5

A) We reject H₀ in favor of H_1, which states the median difference in pain scores before and after treatment are not equal because 1 is less than the critical value 6 for a Wilcoxon signed-ranks test with a population of only 9 individuals.

B) We reject H₀ in favor of H_1, which states the median difference in pain scores before and after treatment are not equal because 1 is greater than the critical value 6 for a Wilcoxon signed-ranks test with a population of only 9 individuals.

C) We fail to reject H_0, which states the median difference in the pain scores before and after treatment are equal because 40 is less than the critical value 6 for a Wilcoxon signed-ranks test with a population of only 9 individuals.

D) We fail to reject H_0, which states the median difference in the pain scores before and after treatment are equal because 40 is greater than the critical value 6 for a Wilcoxon signed-ranks test with a population of only 9 individuals.

True/False

1. True or False? A Kruskal-Wallis test is used to compare a continuous outcome in more than two independent samples.

2. True or False? H₀ for a Mann-Whitney U test is always that the two populations are not equal.

3. True or False? When performing a Mann-Whitney U test, one should always use the lower value of the calculated U values to compare to the critical U value while making the decision rule.

4. True or False? H₀ for the sign test always states that the mean difference between the matched or paired samples is zero.

5. True or False? The test statistic for a sign test is always the larger of the number of positive or negative signs.