In this exercise involving paired differences, consider that it is reasonable to assume the populations being compared have approximately the same shape and that the distribution of paired differences is approximately symmetric.
A sample of 10 men was used in a study to test the effects of a relaxant on the time required to fall asleep. Suppose data for 10 subjects showing the number of minutes required to fall asleep with and without the relaxant follow.
Subject | Relaxant | |
---|---|---|
No | Yes | |
1 | 14 | 9 |
2 | 12 | 10 |
3 | 21 | 11 |
4 | 8 | 12 |
5 | 11 | 9 |
6 | 7 | 4 |
7 | 8 | 10 |
8 | 11 | 8 |
9 | 13 | 10 |
10 | 9 | 7 |
Use a 0.05 level of significance to determine whether the relaxant reduces the median time required to fall asleep.
State the null and alternative hypotheses.
H0: Median time without relaxant − Median
time with relaxant ≥ 0
Ha: Median time without relaxant − Median time
with relaxant < 0H0: Median time without
relaxant − Median time with relaxant ≤ 0
Ha: Median time without relaxant − Median time
with relaxant > 0 H0:
Median time without relaxant − Median time with relaxant >
0
Ha: Median time without relaxant − Median time
with relaxant = 0H0: Median time without
relaxant − Median time with relaxant = 0
Ha: Median time without relaxant − Median time
with relaxant ≠ 0H0: Median time without
relaxant − Median time with relaxant ≠ 0
Ha: Median time without relaxant − Median time
with relaxant = 0
Find the value of the test statistic.
T + =
Find the p-value. (Round your answer to four decimal places.)
p-value =
What is your conclusion?
Reject H0. There is not sufficient evidence to conclude that the relaxant reduces the median time required to fall asleep.Do not reject H0. There is sufficient evidence to conclude that the relaxant reduces the median time required to fall asleep. Reject H0. There is sufficient evidence to conclude that the relaxant reduces the median time required to fall asleep.Do not reject H0. There is not sufficient evidence to conclude that the relaxant reduces the median time required to fall asleep.
In this exercise involving paired differences, consider that it is reasonable to assume the populations being...
You may need to use the appropriate appendix table or technology to answer this question. In this exercise involving paired differences, consider that it is reasonable to assume the populations being compared have approximately the same shape and that the distribution of paired differences is approximately symmetric. A sample of 10 men was used in a study to test the effects of a relaxant on the time required to fall asleep. Suppose data for 10 subjects showing the number of...
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pls explain each step in detail. especially how to determine the p-value(s). thank you Problem 7- Wilcoxon Signed-Rank test A sample of 10 men was used in a study to test the effects of a relaxant on the time required to fall asleep. Data for 10 subjects showing the number of minutes required to fall asleep with and without the relaxant follows. Calculate the test-statistic (create all necessary columns to the right of the table to show all the working)....
Problem 7- Wilcoxon Signed-Rank test A sample of 10 men was used in a study to test the effects of a relaxant on the time required to fall asleep. Data for 10 subjects showing the number of minutes required to fall asleep with and without the relaxant follows. Calculate the test-statistic (create all necessary columns to the right of the table to show all the working). If the level of significance is 0.05 and the calculated p-value for the test...
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