<PRE><B>Question 132968</B>
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.
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Credits earned	Very uncertain	Somewhat certain   Very certain	Row total
0-9.............12     	               8               3            23
10-59...........8	               4	      10	    22
60 or more	1	               7	      11            19
Col total	21	              19	      24	    64
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Research question, at alpha=.01, is the degree of certainty independent of credits?
Ho: degree of certainty is independent of credits
Ha; they are dependent
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Show how the degrees of freedom are calculated, 
df= (# or rows-1)(# of columns-1) = (3-1)(3-1) = 4
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find the critical value of chi-square
left limit=0.484  ;   right limit= 11.143
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Test statistic using Chi-Sq Test on TI calculator: 
Chi-Sq = 14.7638..
p-value: 0.00521...
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and interpret the p-value.
Only 0.00521 of test results could provide stronger evidence
for rejecting Ho.
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Is the conclusion sensitive to the level of significance chosen?
Well the p-value is close to (1/2)% so Ho would be rejected even
though the level of significance is as small as 1%.
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Cheers,
Stan H.
</PRE>