A college teacher was assigned 5 freshmen advisees. In 2006 he administered an a
ID: 3160678 • 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.
2010
2006
Student
X
Y
A
26
21
B
22
20
C
17
14
D
15
10
E
20
15
. 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
. Identify the appropriate hypotheses
b. Test the hypotheses
c. Identify the critical value
Explanation / Answer
To check the attitude of the 5 freshmen advisees, we will apply t – test, considering difference of means test here.
Hypothesis:
Null (Ho) == the scores of 2006 and 2010 of 5 advisees are same i.e. µ1 = µ2
Alternate (H1) == the scores of 2006 and 2010 of 5 advisees are not same i.e. µ1 µ2
µ1 = 20 and µ2 = 16 [ Calculated]
std deviation of first sample s1 = 4.30 and sample s2 = 4.53 [calculated]
Common Std deviation (s ) = n1 sq of (s1) + n2 sq of (s2)/ n1+n2-2
= 5 X (4.3)2 + 5 X (4.5)2/ 5+5-2 = 24.21
Test statistics t = µ1 - µ2 / s (1/n1+1/n2)
= 20 -16 / 24.21(1/5 +1/5
T (calculated) = 0.26 at degree of freedom (df) = 5+5-2 = 8
The critical value (from the table) at df = 8 (5% level of significance) is = 1.86
Since the t(cal = 0.26 ) is less than t(critical = 1.86)
That’s why we accept the null Hypothesis (H0) means the attitude in 2006 and 2010 are same.
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