Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. At α = .01, is the degree of certainty independent of credits earned? |
Credits Earned |
Very Uncertain |
Somewhat Certain |
Very Certain |
Row Total | ||||||||||||||||||||||||||||||||||||
0 – 9 | 12 | 9 | 3 | 24 | ||||||||||||||||||||||||||||||||||||
10 – 59 | 8 | 3 | 9 | 20 | ||||||||||||||||||||||||||||||||||||
60 or more | 1 | 7 | 12 | 20 | ||||||||||||||||||||||||||||||||||||
Col Total | 21 | 19 | 24 | 64 | ||||||||||||||||||||||||||||||||||||
|
a)
Yes
b)
applying chi square test of independence:
Expected | Ei=Σrow*Σcolumn/Σtotal | very uncertan | somewhat | very certain | Total |
0-9 | 7.875 | 7.125 | 9.000 | 24 | |
10-59 | 6.563 | 5.938 | 7.500 | 20 | |
60 or more | 6.563 | 5.938 | 7.500 | 20 | |
Total | 21 | 19 | 24 | 64 | |
chi square χ2 | =(Oi-Ei)2/Ei | very uncertan | somewhat | very certain | Total |
0-9 | 2.161 | 0.493 | 4.000 | 6.654 | |
10-59 | 0.315 | 1.453 | 0.300 | 2.068 | |
60 or more | 4.715 | 0.190 | 2.700 | 7.605 | |
Total | 7.190 | 2.137 | 7.000 | 16.327 |
Test statistic=16.33
d.f.=(row-1)*(column-1)=(3-1)*(3-1)=4
p value =0.0026
c)
Critical value=13.28
d)
Yes
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