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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=
Business College
Mean = np =300*0.3= 90
Standard Deviation= s= =
= 7.94
Arts College
Mean = np =300*0.4= 120
Standard Deviation= s= =
= 8.49
Education College
Mean = np =300*0.3= 90
Standard Deviation= s= =
= 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.