PRACTICE OF STATS - 1 TERM ACCESS CODE
4th Edition
ISBN: 9781319403348
Author: BALDI
Publisher: Macmillan Higher Education
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Question
Chapter 27, Problem 27.35E
To determine
To explain is there evidence of significant improvement within each group and did the treatment group show significantly greater improvement then the control group.
Expert Solution & Answer
Answer to Problem 27.35E
Yes, there is evidence of significant improvement within each group but the treatment group showno significantly greater improvement then the control group.
Explanation of Solution
In the question, it is given the scores of the mathematical skills before and after a subliminal message for both the treatment group and control group. Now, to find that whether there evidence of significant improvement within each group, we will perform the Wilcoxon signed rank test for each group by the software. Thus, by performing the Wilcoxon signed rank test for the treatment group let us first find the difference and then the results for the test by software are as follows:
Null hypothesis: There is no difference between them.
Alternative hypothesis: There is evidence of significant improvement within group.
| Treatment | ||
| Before | After | Difference Treatment |
| 18 | 24 | -6 |
| 18 | 25 | -7 |
| 21 | 33 | -12 |
| 18 | 29 | -11 |
| 18 | 33 | -15 |
| 20 | 36 | -16 |
| 23 | 34 | -11 |
| 23 | 36 | -13 |
| 21 | 34 | -13 |
| 17 | 27 | -10 |
| Data | Rank |
| -6 | 1 |
| -7 | 2 |
| -12 | 6 |
| -11 | 4.5 |
| -15 | 9 |
| -16 | 10 |
| -11 | 4.5 |
| -13 | 7.5 |
| -13 | 7.5 |
| -10 | 3 |
| variables: | Before - After |
| 0 | sum of positive ranks |
| 55 | sum of negative ranks |
| 10 | n |
| 27.50 | |
| 9.50 | standard deviation |
| -2.89 | z, corrected for ties |
| .0019 | p-value (one-tailed, lower) |
As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,
Thus, we have sufficient evidence to conclude that there is evidence of significant improvement within treatment group.
Thus, now by performing the Wilcoxon signed rank test for the control group let us first find the difference and then the results for the test by software are as follows:
Null hypothesis: There is no difference between them.
Alternative hypothesis: There is evidence of significant improvement within group.
| Control | ||
| Before | After | Difference Control |
| 18 | 29 | -11 |
| 24 | 29 | -5 |
| 20 | 24 | -4 |
| 18 | 26 | -8 |
| 24 | 38 | -14 |
| 22 | 27 | -5 |
| 15 | 22 | -7 |
| 19 | 31 | -12 |
| Data | Rank |
| -11 | 6 |
| -5 | 2.5 |
| -4 | 1 |
| -8 | 5 |
| -14 | 8 |
| -5 | 2.5 |
| -7 | 4 |
| -12 | 7 |
| variables: | Before - After |
| 0 | sum of positive ranks |
| 36 | sum of negative ranks |
| 8 | n |
| 18.00 | expected value |
| 6.93 | standard deviation |
| -2.60 | z, corrected for ties |
| .0047 | p-value (one-tailed, lower) |
As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,
Thus, we have sufficient evidence to conclude that there is evidence of significant improvement within control group.
Now, to find did the treatment group show significantly greater improvement then the control group, we will use the Wilcoxon rank sum test by using the software. Thus, the hypotheses will be defined as:
Null hypothesis: The treatment group show no significant improvement then the control group.
Alternative hypothesis: The treatment group show significantly greater improvement then the control group.
| Label | Data | Rank |
| Difference Treatment | -6 | 15 |
| Difference Treatment | -7 | 13.5 |
| Difference Treatment | -12 | 6.5 |
| Difference Treatment | -11 | 9 |
| Difference Treatment | -15 | 2 |
| Difference Treatment | -16 | 1 |
| Difference Treatment | -11 | 9 |
| Difference Treatment | -13 | 4.5 |
| Difference Treatment | -13 | 4.5 |
| Difference Treatment | -10 | 11 |
| Difference Control | -11 | 9 |
| Difference Control | -5 | 16.5 |
| Difference Control | -4 | 18 |
| Difference Control | -8 | 12 |
| Difference Control | -14 | 3 |
| Difference Control | -5 | 16.5 |
| Difference Control | -7 | 13.5 |
| Difference Control | -12 | 6.5 |
| n | sum of ranks | |
| 10 | 76 | Difference Treatment |
| 8 | 95 | Difference Control |
| 18 | 171 | total |
| 95.00 | expected value |
| 11.21 | standard deviation |
| -1.65 | z, corrected for ties |
| .9506 | p-value (one-tailed, upper) |
As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,
Thus, we have no sufficient evidence to conclude that the treatment group show significantly greater improvement then the control group.
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Chapter 27 Solutions
PRACTICE OF STATS - 1 TERM ACCESS CODE
Ch. 27 - Prob. 27.1AYKCh. 27 - Prob. 27.2AYKCh. 27 - Prob. 27.3AYKCh. 27 - Prob. 27.4AYKCh. 27 - Prob. 27.5AYKCh. 27 - Prob. 27.6AYKCh. 27 - Prob. 27.7AYKCh. 27 - Prob. 27.8AYKCh. 27 - Prob. 27.9AYKCh. 27 - Prob. 27.10AYK
Ch. 27 - Prob. 27.11AYKCh. 27 - Prob. 27.12AYKCh. 27 - Prob. 27.13AYKCh. 27 - Prob. 27.14AYKCh. 27 - Prob. 27.15AYKCh. 27 - Prob. 27.16AYKCh. 27 - Prob. 27.17AYKCh. 27 - Prob. 27.18AYKCh. 27 - Prob. 27.19AYKCh. 27 - Prob. 27.20AYKCh. 27 - Prob. 27.21AYKCh. 27 - Prob. 27.22AYKCh. 27 - Prob. 27.23AYKCh. 27 - Prob. 27.24AYKCh. 27 - Prob. 27.25CYSCh. 27 - Prob. 27.26CYSCh. 27 - Prob. 27.27CYSCh. 27 - Prob. 27.28CYSCh. 27 - Prob. 27.29CYSCh. 27 - Prob. 27.30CYSCh. 27 - Prob. 27.31CYSCh. 27 - Prob. 27.32CYSCh. 27 - Prob. 27.33CYSCh. 27 - Prob. 27.34CYSCh. 27 - Prob. 27.35ECh. 27 - Prob. 27.36ECh. 27 - Prob. 27.37ECh. 27 - Prob. 27.38ECh. 27 - Prob. 27.39ECh. 27 - Prob. 27.40ECh. 27 - Prob. 27.41ECh. 27 - Prob. 27.42ECh. 27 - Prob. 27.43ECh. 27 - Prob. 27.44ECh. 27 - Prob. 27.45ECh. 27 - Prob. 27.46ECh. 27 - Prob. 27.47ECh. 27 - Prob. 27.49ECh. 27 - Prob. 27.50ECh. 27 - Prob. 27.51E
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