Question

Below is a two-way table which describes the breakdown of majors by gender

	MALES	FEMALES	Total
SCIENCE	29	85	114
ENGINEERING	41	91	132
BUSINESS	63	123	186
LIBERAL ARTS	58	79	137
Total

a. Which type of test should be carried out to test the hypothesis that there is no association between major and gender in the source population,?                            [ Select ]                       ["Goodness of fit", "Test of indpepndence"]      

b. the appropriate test statistic is                            [ Select ]                       ["chi-square", "t statistic", "z statistic"]         with degrees of freedom equal to                            [ Select ]                       ["3", "3 and 1", "568", "not applicable"]         .

c. The critical value at alpha = .05 to test the above test of hypothesis is                            [ Select ]                       ["7.815", "0.037", "8.48", "9.348"]      

d. The critical value at alpha = .05 to test the hypothesis that proportion of all majors are the same is                            [ Select ]                       ["9.348", "8.48", "0.037", "7.815"]         .

Answer 1

Solution:-

(a) “Test of independence” is suitable to test that there is no association between major and gender in the source population.

(b) “Chi-square test of independence” is the appropriate test statistic as The Chi-Square test of independence is used to determine if there is a significant relationship between two nominal (categorical) variables. The frequency of each category for one nominal variable is compared across the categories of the second nominal variable.

With degrees of freedom = (c-1)*(r-1)

Where,

           r = No. of rows & c = No. of columns

Hence,

           Degree of freedom = (2-1)*(4-1) = 3.

(c) The critical value from the table is given by:-

    χ2 (α=0.05&DF=3) = 7.815

(d) The appropriate test to test the hypothesis that proportions of all majors are the same is “Chi-square goodness of fit”.

Hence,

            The critical value from the table is given by:-

           χ2 (α=0.05&DF=3) = 7.815