1 answer

Explain if possible You are interested in investigating whether gender and major are associated at your...

Question:

Explain if possible
You are interested in investigating whether gender and major are associated at your college. The table below shows the result
H: III Expected College major and gender are independent. The distribution of college major is not the same for each gender.
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
H: III Expected College major and gender are independent. The distribution of college major is not the same for each gender. The distribution of college major is the same for each gender. O College major and gender are dependent. c. The test-statistic for this data = (Please show your answer to three decimal places.) d. The p-value for this sample = (Please show your answer to four decimal places.) e. The p-value is Select an answer chi squa f. Based on this, we should O accept the null O reject the null O fail to reject the null fro abov Commen g. Thus, the final conclusion is... p value There is sufficient evidence to conclude that college major and gender are independent. Conclus differen There is insufficient evidence to conclude that the distribution of college major is not the same for each gender There is insufficient evidence to conclude that college major and gender are dependent. There is sufficient evidence to conclude that college major and gender are dependent. There is sufficient evidence to conclude that the distribution of college major is not the same for each gender ons v

Answers

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

(b).

  • Null Hypothesis (Ho) : 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 &.</p><p>( fiij- eij eij анализ where tii Obseened to iti sol & itNow 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;)? eigExpected Values maths/science arts/humanities business/econ. other Total 1862 288 = 84.494 230x298 = 104.482 656 152298 = 69.Squared Distances maths/science arts/humanities business/econ. other men (75-54.494) 84.494 = 1.067 (101-104.482) 104.482 0.1yre 1.067 + 0.888 + 0.116 + 0.097 + 0.055 + 0.046 + 3.04 + 2.531 x² 7. 839.</p><p>(d) Based on the information provided, x=0005, deدری Thus final conclusion is : nown There suth scient Evidence to conclude that college gender are dependent Ps sufficient ma

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