The following data was collected as part of a study examining whether there is a difference between the number of hours men and women watch television. The values represent the number of hours a subject watched television on a designated Monday night. Lower values rank ahead of higher ones. Calculate , , and the z test value for the Wilcoxon rank sum test.

Question

The following data was collected as part of a study examining whether there is a difference between the number of hours men and women watch television. The values represent the number of hours a subject watched television on a designated Monday night. Lower values rank ahead of higher ones.  Calculate  ,  , and the z test value for the Wilcoxon rank sum test.

Quizplus · Accepted Answer

To find the median for both groups, we need to first arrange the data in order:
Women: 1.5 2 2.5 3 3.5 4 4 4.5 5 6
Men: 1 2 2 2.5 3.5 4 4 4.5 5

The median for women is the middle value, which is 4 hours.
The median for men is also 4 hours.

Therefore 11eaa984_72d1_2e0b_97c0_cdd7772c752f_TB1705_00 is not correct, as there is not a difference in median number of hours watched between men and women.

To calculate the Wilcoxon rank sum test:
- Rank all the values together in order from lowest to highest (ties get averaged ranks). 
- Sum up the ranks of the values for the women's group (W) and men's group (M)
- Calculate the z-score using the following formula: z = (lower sum - (n(n+1))/2) / sqrt(n(n+1)(2n+1)/6)
  where n is the total sample size (n = 19 in this case) and the lower sum is the sum of the ranks for the group with the smaller sum (W in this case)

Ranking all values, we get:
1 1.5 2 2 2.5 3 3 3.5 4 4 4 4.5 4.5 5 5 6 7 8 9
W: 2 3 5 6 8 9 10 12 14 19
M: 1 4 7 11 13 15 16 18

The sum of the ranks for W is 95.
The sum of the ranks for M is 85.

Since the women's sum is lower, we use that in the formula.
z = (lower sum - (n(n+1))/2) / sqrt(n(n+1)(2n+1)/6)
z = (95 - (19(20))/2) / sqrt(19(20)(39)/6)
z = -1.222

Looking up the z-score in a standard normal distribution table (or using a calculator), we find the p-value to be 0.109.
Since this is greater than the typical alpha level of 0.05, we fail to reject the null hypothesis and conclude that there is not significant evidence to suggest a difference between the number of hours men and women watch television.

The Following Data Was Collected as Part of a Study