Question

	Males	Females	Total
Like Sociology	30	80	110
Not Like Sociology	70	20	90
Total	100	100	200

Using this table, write assumptions, hypotheses, and suggest appropriate tests for the testing of the hypotheses.

(I'm sorry, this is all the information I was given for the answer!)

Answer 1

Making a lot of assumption, here is the chi-square test of independence.

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 Sociology preference are independent Ha​: The two variables - Gender and Sociology preference 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​>50.5051)=0 (6)The decision about the null hypothesis Since it is observed that χ2=50.5051>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 Sociology preference 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.