Question

In a study on students’ intention to apply for graduate school, a researcher is interested in the difference between Sociology majors and Justice Studies majors at a large state university. The research hypothesizes that the proportion of sociology majors who intend to apply for graduate schools is higher than that of Justice Studies majors. To test this hypothesis, the research interviews 60 juniors and seniors majoring in sociology and 105 in Justice Studies majors. Of the 60 sociology majors, 35 say that they are considering applying; and of the 105 Justice majors, 40 say that are considering applying. Sociology Justice Studies N1 = 60 N2 = 105 f1 = 35 f2 = 40 Please test the hypothesis stated above (i.e. the proportion of sociology majors who are considering applying for graduate school is higher than the proportion of Justice Studies majors.) (10 points). (Note: this is a hypothetical research situation and none of the statistics presented in the above table is “real.”)

Answer 1

Let p₁ = The proportion of Sociology Majors who intend to apply to graduate school = 35/60 = 0.5833

Let p₂ = The proportion of Justice Studies Majors who intend to apply to graduate school = 40/105 = 0.3810

Let = Overall proportion = (35+40)/60+105) = 75/165 = 0.4545

1 - = 0.5455

= Default level (as nothing is mentioned) = 0.05

(a) The Hypothesis:

H0: p₁ = p₂ : The proportion of Sociology Majors who intend to apply to graduate school is equal to the proportion of Justice Studies Majors who intend to apply to graduate school.

Ha: p₁ > p₂ : The proportion of Sociology Majors who intend to apply to graduate school is greater than the proportion of Justice Studies Majors who intend to apply to graduate school.

This is a 1 Tailed, Right Tailed Test.

The Test Statistic:

The p Value: The p value (Right) for Z = 2.52, is; p value = 0.0059

The Critical Value: The critical value (1 tail) at = 0.05, Zcritical = + 1.645

The Decision Rule:    If Zobserved is > Zcritical, Then Reject H0.

Also If the P value is < , Then Reject H0

The Decision: Since Z observed (2.52) is > Zcritical (1.645), We Reject H0.

Also since P value (0.0059) is < (0.05), We Reject H0.

The Conclusion: There is sufficient evidence at the 95% significance level to conclude that the proportion of Sociology Majors who intend to apply to graduate school is greater than the proportion of Justice Studies Majors who intend to apply to graduate school.