Question

Explain if possible

You are interested in investigating whether gender and major are associated at your college. The table below shows the results of a survey. Other Frequencies of Majors and Gender Math/Science Arts/Humanities Business/Econ. 75 101 71 111 129 81 Men Women 51 37 What can be concluded at the a = 0.05 significance level? a. What is the correct statistical test to use? O Independence O Paired t-test O Homogeneity O Goodness-of-Fit b. What are the null and alternative hypotheses? HO: O The distribution of college major is the same for each gender. The distribution of college major is not the same for each gender. O College major and gender are independent. College major and gender are dependent

Answer 1

(a). Since we have to access degree of association between categorical variables. Therefore we use chi-square test of independence.

(b).

• Null Hypothesis (H_o) : College major and gender are independent
• Alternative Hypothesis (H₁) : College major and gender are dependent

(c).

Test of Independence Statistic for chi-sq. Test given РЯ is 2. й &. ( fiij- eij eij анализ where tii Obseened to iti sol & ith Colunm corresponding мара ча corresponding eij • Expected to pri socor Column. --- follows x²-variale with (-1) (s- 1) reedom. freedom number ol и и040 jous num в Column. %

Now or eij is computed by eijs = Ri xej where ith row Ri total sum of 0 total Sum c of ith column total Cerand T

. -Test Statistic x SE C fij - ei;)? eig

Expected Values maths/science arts/humanities business/econ. other Total 1862 288 = 84.494 230x298 = 104.482 656 152298 = 69.049 men 88x298 656 656 656 = 39.976 298 186x368 = 101.506 230x358 = 125.518 152 358 = 82.951 women 88X358 656 = 48.024 358 658 656 656 Total 186 230 152 88 656

Squared Distances maths/science arts/humanities business/econ. other men (75-54.494) 84.494 = 1.067 (101-104.482) 104.482 0.116 (71-69.049) 69.09 = 0.055 (51-39.976) 39.976 = 3.04 women (111-101.506) 101.506 0.888 (129-125.518) 125518 0.097 (81-82.951) 82.961 = 0.046 (37-48.024) 48.024 = 2.531

yre 1.067 + 0.888 + 0.116 + 0.097 + 0.055 + 0.046 + 3.04 + 2.531 x² 7. 839. (d) Based on the information provided, x=0005, degree of freedom = (2-1) 04-) = 3. so the correspo ponding 3 > 7.8 39) p-value = P( X = 0.0495 ce) p-value is less than 0.05 (8) we. Should reject the null

دری Thus final conclusion is : nown There suth scient Evidence to conclude that college gender are dependent Ps sufficient major and