3. Consid the effectiveness of a asth ra er a Phase II clinical trial designed t

Question

3. Consid the effectiveness of a asth ra er a Phase II clinical trial designed to investigate ma in children. A total of n=10 participants are new drug to reduce symptoms ndomized to receive either the new drug or a placebo. articipants are asked to record the number of episodes of shortness of breath over a 1 week period following receipt of the assigned treatment. The data are shown below. (a) At a 5% significance level, use th Mann-Whitney U-Test to test the hypothesis that there was no difference in the number of episodes of shortest of breath between the placebo and New Drug/ (b) Show Critical Values and make a statistical Decision. (c) Write a one-sentence conclusion. Data Follows: Placebo New Drug 3 6 4 2 4 12 Mean 6.8 SD 3.11 3.2 1.92

Explanation / Answer

Answer:

Our Hypothesis is,

H0:There was no difference in the number of episodes of shortest of breath between the placebo and New Drug

H1: There was a differance in the number of episodes of shortest of breath between the placebo and New Drug

Level of Significance=0.05

Placebo
Sum of ranks: 37
Mean of ranks: 7.4
Expected sum of ranks: 27.5
Expected mean of ranks: 5.5
U-value: 3
Expected U-value: 12.5

New Drug
Sum of ranks: 18
Mean of ranks: 3.6
Expected sum of ranks: 27.5
Expected mean of ranks: 5.5
U-value: 22
Expected U-value: 12.5

Both Combined
Sum of ranks: 55
Mean of ranks: 5.5
Standard Deviation: 4.7871

So, The U-value is 3.

b) The critical value of U at p < .05 is 2.

Therefore, the result is not significant at p < .05.

The Z-Score is 1.88004. The p-value is .0601.

So, The result is not significant at p < .05.

The approximation to the form of the normal distribution becomes less robust at sample sizes smaller than 10, so caution is appropriate here in making use the Z-value calculation.

c) Conclusion: We fail to reject Null hypothesis H0. So,we conclude that, There was no difference in the number of episodes of shortest of breath between the placebo and New Drug.

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