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# Hypothesis Test of gender differences

II. In a sample of 664 patients who received this training, suppose that 47 showed reduced allergic reactions and 17 showed increased allergic reactions. Are these results sufficient to conclude that the self hypothesis has a significant effect. Assume that increasing and decreasing allergic reactions are equally likely if the training has no effect. Use alpha = 0.05.

III. Gender differences in dream content are well documented (see Winget & Kramer, 1979). Suppose a researcher studies aggression content in the dreams of men and women. Each participant reports his or her most recent dream. Then each dream is judged by a panel of experts to have low, medium, or high aggression content. The observed frequencies are shown in the following matrix:

Low Medium High

Gender Female 18 4 2

Male 4 17 15

Is there a relationship between gender and the aggression content of dreams? Test with alpha = 0.01.

#### Solution Preview

Please refer to the attachments for the solution. Thank You.

Solution-I:
Null Hypothesis: The self hypothesis has no significant effect in reducing allergic reactions.
H_0: p≤0.5
Alternate Hypothesis: The self hypothesis has significant effect in reducing allergic reactions.
H_1:p>0.5
Analysis Plan:
We shall use z hypothesis test for proportion to test the given hypothesis.
Level of significance, α = 0.05.

Critical Value and Decision Rule:
Since the alternate hypothesis is given as H_1:p>0.5, this is an upper-tailed test.
The critical value of z for an upper tailed test of proportion for a significance level of 0.05 ...

#### Solution Summary

This solution is comprised of a detailed explanation of the various aspects of Hypothesis Tests as they pertain to the given problems. Supplemented with Interactive EXCEL sheet, the solution provides students with a clear perspective of the calculations and underlying concepts.

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