A college teacher was assigned 5 freshmen advisees. In 2006 he administered an a
ID: 3160680 • Letter: A
Question
A college teacher was assigned 5 freshmen advisees. In 2006 he administered an attitude scale that measured liberalism-conservatism. Four years later in 2010, just before graduation, all 5 took the same scale again. Are the attitudes the same? The scores below were obtained. Identify and test the appropriate hypotheses at the .05 level of significance.
. Identify the appropriate hypotheses
b. Test the hypotheses
c. Identify the critical value
2010
2006
Student
X
Y
A
26
21
B
22
20
C
17
14
D
15
10
E
20
15
2010
2006
Student
X
Y
A
26
21
B
22
20
C
17
14
D
15
10
E
20
15
Explanation / Answer
We need to test the equality means of scores of students in the years 2006 and 2010.
Mean2006 = 80/5 = 16
Mean2010 = 100/5 = 20
Std Dev 2006 = 4.53
Std Dev 2010 = 4.30
T = (Mean2010 - Mean 2006)/((S2010^2/5 + S2006^2/5)^0.5)
= 4/2.79 = 1.433
Degrees of freedom = 8
So critical value is t8,0.975 = 2.306 < T
Hence null hypothesis that means are equal cannot be rejected.
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