Question

A recent study of undergraduates looked at gender differences in dieting trends. The following table summarizes whether a student tried a low-fat diet or not by gender:

Tried low-fat diet	Women	Men
Yes	35	8
No	146	97

At the 0.05 level of significance, is there evidence to conclude that there is a relationship between gender and the likelihood of trying a low-fat diet?

Answer 1

Chi-Square Independence test - Results

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0​: The two variables - Gender and Likelihood of trying a low fat diet are independent Ha​: The two variables - Gender and Likelihood of trying a low fat diet are dependent This corresponds to a Chi-Square test of independence. (2) Degrees of Freedom The number of degrees of freedom is df = (2 - 1) * (2 - 1) = 1 (3) Critical value and Rejection Region Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df = (2 - 1) * (2 - 1) = 1, so the critical value is 3.8415. Then the rejection region for this test becomes R={χ2:χ2>3.8415}. (4)Test Statistics The Chi-Squared statistic is computed as follows: (5)P-value The corresponding p-value for the test is p=Pr(χ2​>7.1427)=0.0075 (6)The decision about the null hypothesis Since it is observed that χ2=7.1427>χ2_c​rit=3.8415, it is then concluded that the null hypothesis is rejected. (7)Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables - Gender and Likelihood of trying a low fat diet are dependent, at the 0.05 significance level. Conditions: a. The sampling method is simple random sampling. b. The data in the cells should be counts/frequencies c. The levels (or categories) of the variables are mutually exclusive.

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