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Chi square test of independence and test for goodness

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In a sample of 64 patients, suppose that 47 showed allergic reduced reaction and 17 show increased reaction. Are these results sufficient to conclude a significant effect? Assume that increasing and decreasing reactions are equally likely if the training had no effect. Use alpha .05

gender difference in dream content
female low medium high
18 4 2
male 4 17 15

Is there a relationship between gender and the aggression content of dreams? Test with alpha .01

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This solution goes through statistical methods such as the chi square test for independence and test for goodness of fit

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