Question

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Using α = .05, the conclusion of the test is that the a. proportions have not changed significantly. b. proportions follow normal distribution. c. Marascuilo procedure is more applicable. d. null hypothesis cannot be rejected.

Answer 1

Answer:

a. proportions have not changed significantly

Step-by-step explanation:

Given

Business College= 35 %

Arts College= 35 %

Education College = 30%

Calculated

Business College = 90/300= 9/30= 0.3 or 30%

Arts College= 120/300= 12/30= 2/5= 0.4 or 40%

Education College= 90/300= 9/30 = 0.3 or 30%

First we find the mean and variance of the three colleges using the formulas :

Mean = np

Standard Deviation= s= $\sqrt{npq\\}$

Business College

Mean = np =300*0.3= 90

Standard Deviation= s= $\sqrt{npq\\}$=$\sqrt{0.3*0.7*300}$= 7.94

Arts College

Mean = np =300*0.4= 120

Standard Deviation= s= $\sqrt{npq\\}$=$\sqrt{0.4*0.6*300}$=  8.49

Education College

Mean = np =300*0.3= 90

Standard Deviation= s= $\sqrt{npq\\}$=$\sqrt{0.3*0.7*300}$= 7.94

Now calculating the previous means with the same number of students

Business College

Mean = np =300*0.35= 105

Arts College

Mean = np =300*0.35= 105

Education College:

Mean = np =300*0.3= 90

Now formulate the null and alternative hypothesis

Business College

90≤ Mean≥105

Arts College

105 ≤ Mean≥ 120

Education College

U0 : mean= 90     U1: mean ≠ 90

From these we conclude that the  proportions have not changed significantly meaning that it falls outside the critical region.