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 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. B) 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. C) 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. D) 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.

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Question

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 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.
B) 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.
C) 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.
D) 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.

Chemotherapy
Patient
Before
After
Difference
Sign
Treatment
Treatment
1
9.
3
2
12
3
14
7
4
9.
4
8.
2
6.
11
3
7
15
7
8
12
8.
7
8.
10
5
11
8.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Expert Solution

Step 1

The null and alternative hypothesis are :

$H_{o} : T h e r e i s n o d i f f e r e n c e i n s y m p t o m s b e f o r e a n d a f t e r t r e a t m e n t . H_{o} : P (+) = P (-) H_{1} : T h e r e i s a s i g n i i c a n t d i f e r e n c e i n s y m p t o m s b e f o r e a n d a f t e r t r e a t m e n t . H_{1} : P (+) > P (-)$

[Note : More positive signs will indicate that the new medication or treatment in effective which helped reducing the number of times a chemotherapy patient vomits.]

Procedure,

Calculate the difference between before treatment and after treatment. Assign the signs to these differences. If the plus and minus signs are similar then it can be said that the both populations are symmetric. But if there are too many plus signs as compared to minus signs or vice versa, then the null hypothesis is rejected.

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