Question

Nasser who is a medical doctor at Swan Hospital believed that the average relief times when taking the Devino pain killer is 110 minutes. A random sample of 15 patients with a severe joint pain were selected and were given the Devino medicine. The time it took each patient to feel pain-free is given below

100 125 150 160 185 125 155 145 160 100 150 140 135 120 110

(a) Using the Wilcoxon signed ranks test, can we conclude that the median relief time is actually slower than the claimed value? (Hint: use the average as the median and use alpha = 0.05)

(b)  Suppose I gave you: sample mean=137.333 and sample variance=581.6667. Assuming normality and using information from part (a), compute the p-value.

Answer 1

(a) W-value: 4
Mean Difference: 29.29
Sum of pos. ranks: 101
Sum of neg. ranks: 4

Z-value: -3.0447
Mean (W): 52.5
Standard Deviation (W): 15.93

Sample Size (N): 14

Result 1 - Z-value

The value of z is-3.0447. The p-value is .00236.

The result is significant at p < .05.

Result 2 - W-value

The value of W is 4. The critical value for W at N = 14 (p < .05) is 15.

The result is significant at p < .05.

It suggests that,

The median relief time is actually slower than the claimed value

b)

Z = (X - μ) / σ
Z = (137.333 - 110) / 24.1177

Z = 1.13332

The P-Value is .128544.

The result is not significant at p < .05.