Question

You are curious about the role of graduate status on work-life balance in Tech students. In a sample of 100 undergraduate students, 37 reported having trouble balancing school and work. In a separate sample of 75 graduate students, 50 had trouble with this balance. Test the null hypothesis that undergraduate or graduate students are equally likely to have trouble with work-life balance (alpha=0.05).

For independent sample t-tests: mean values for each sample, the variances for each sample, estimated standard error of the difference in means, the t-ratio, degrees of freedom, the t-critical value, and your decision to reject or retain the null.

For dependent sample t-tests: mean values for each sample, standard deviation for the difference between groups, standard error of the difference between the means, the t-ratio, degrees of freedom, the t-critical value, and your decision to reject or retain the null.

For proportions: sample proportions, combined proportions, standard error of the difference, z-score, critical z-score, and your decision to reject or retain the null.

Answer 1

p₁ : Proportion of undergraduate students who have trouble balancing school and and work

p₂ : Proportion of graduate students who have trouble balancing school and and work

Null hypothesis : H_o : p₁ = p₂

Alternate Hypothesis : H_a : p₁ p₂

Two-tailed test

Given,

In a sample of 100 undergraduate students, 37 reported having trouble balancing school and work

Sample size for undergraduate students: n₁ = 100

Number of reported having trouble balancing school and and work of the undergraduate student sample :x₁ = 37

Sample Proportion of undergraduate students who have trouble balancing school and and work : = 37/100 =0.37

In a separate sample of 75 graduate students, 50 had trouble with this balance

Sample size for graduate students: n₂ = 75

Number of reported having trouble balancing school and and work of the graduate student sample :x₂ = 50

Sample Proportion of graduate students who have trouble balancing school and and work : = 50/75 =0.6667

Sample Proportions :

Sample Proportion of undergraduate students who have trouble balancing school and and work : = 37/100 =0.37

Sample Proportion of graduate students who have trouble balancing school and and work : = 50/75 =0.6667

combined proportion

Standard error of the Difference : SE

Standard error of the Difference: SE =0.0764

Z-score :

Z-score = -3.8848

Critical Z-score for Two Tailed test:Given Alpha : =0.05

As Z-score is less than Critical Z-score i.e. ( -3.88<-1.96 ); Reject Null Hypothesis.

Reject the null.