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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

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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