(a)
To find the
(a)
Answer to Problem 27.1AYK
Explanation of Solution
In the question, it is given the table for the subjects spent standing or walking over a ten-day period. It concerned a study comparing the level of physical activity of lean and mildly obese people who do not exercise. The data are a bit irregular but not distinctly non-Normal. Let us use the Wilcoxon test for comparison with the two-sample t test. Now, to find the median minutes spent standing or walking for each group, let us arrange the whole data in ascending order and the bold ones are lean subjects. Then the data will be as:
260.244 |
267.344 |
319.212 |
347.375 |
358.65 |
367.138 |
374.831 |
410.631 |
413.667 |
416.531 |
426.356 |
464.756 |
504.7 |
511.1 |
543.388 |
555.656 |
578.869 |
584.644 |
607.925 |
677.188 |
Now, the median is calculated as:
And as we can see that the last part of the data contains the lean subjects more so their physical activities are more than the obese subjects. Thus, lean subjects are more active.
(b)
To arrange all twenty observations in order and find the ranks.
(b)
Explanation of Solution
In the question, it is given the table for the subjects spent standing or walking over a ten-day period. It concerned a study comparing the level of physical activity of lean and mildly obese people who do not exercise. The data are a bit irregular but not distinctly non-Normal. Let us use the Wilcoxon test for comparison with the two-sample t test. Now let us arrange all data in order and gave rank by using excel by clicking on the sort icon in the home tab. The data with the ranks will be as:
Rank | Subjects |
1 | 260.244 |
2 | 267.344 |
3 | 319.212 |
4 | 347.375 |
5 | 358.65 |
6 | 367.138 |
7 | 374.831 |
8 | 410.631 |
9 | 413.667 |
10 | 416.531 |
11 | 426.356 |
12 | 464.756 |
13 | 504.7 |
14 | 511.1 |
15 | 543.388 |
16 | 555.656 |
17 | 578.869 |
18 | 584.644 |
19 | 607.925 |
20 | 677.188 |
(c)
To find out what is the value of W and if null hypothesis is true what are the mean and standard deviation of W .
(c)
Answer to Problem 27.1AYK
The value W is
Explanation of Solution
In the question, it is given the table for the subjects spent standing or walking over a ten-day period. It concerned a study comparing the level of physical activity of lean and mildly obese people who do not exercise. The data are a bit irregular but not distinctly non-Normal. Let us use the Wilcoxon test for comparison with the two-sample t test.The ranks are given in part (b), so let us sum the ranks for the subjects. Then we have,
Subjects | Sum |
Lean subjects | 142 |
Obese subjects | 68 |
Now, the value Wis
Null hypothesis: There is no difference in the distribution of subjects.
Alternative hypothesis: Lean subjects are higher than the obese subjects.
And the mean and standard deviation is calculated as:
Now let us calculate the P-value as:
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 prove that the lean subjects spent more minutes standing or walking than the obese subjects.
(d)
To explain does comparing W with the mean and standard deviation suggest that the lean subjects are more active than the obese subjects.
(d)
Answer to Problem 27.1AYK
No, comparing W with the mean and standard deviation does not suggest that the lean subjects are more active than the obese subjects.
Explanation of Solution
In the question, it is given the table for the subjects spent standing or walking over a ten-day period. It concerned a study comparing the level of physical activity of lean and mildly obese people who do not exercise. The data are a bit irregular but not distinctly non-Normal. Let us use the Wilcoxon test for comparison with the two-sample t test. The ranks are given in part (b), so let us sum the ranks for the subjects. Then we have,
Subjects | Sum |
Lean subjects | 142 |
Obese subjects | 68 |
And the mean and standard deviation is calculated as:
Thus, comparing W with the mean and standard deviation does not suggest that the lean subjects are more active than the obese subjects because there is less difference between the value of W from the mean of W . so, we do not have a strong evidence from this that the lean subjects are more active than the obese subjects.
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Chapter 27 Solutions
ACHIEVE F/PRACT OF STAT IN LIFE-ACCESS
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