
WINNER * WHERE Crosstabulation 

Count 
WHERE:: 

WINNER: 
east 
west 
Total 
bush 
13 
17 
30 
gore 
13 
7 
20 
Total 
26 
24 
50 
ChiSquare Test
Value 
df 
Asymp. Sig. (2sided) 

Pearson ChiSquare 
2.257 


N of Valid Cases 
50 
a) 15.6, found by multiplying
30 by 26 and dividing by 50. (Bush won 60% of the states
(30/50). If geography makes no difference, he would have won
60% of the eastern states. 60% of 26 is 15.6.)
b) Not at usual levels. If location does not matter, we
would get results as different from the expected values over
13% of the time. So random chance is a plausible explanation
for the differences from the expected
breakdown.
2. A researcher has surveyed a large number of high schools trying to determine their attitudes toward college. One question is whether or not they have ever heard of Saint Joseph's College. The researcher suspects that as students advance through high school, they learn more about colleges, and hence seniors should be more likely to have heard of Saint Joseph's College than freshmen. She decides to test this hypothesis using ChiSquare. Below are the results she gets:
QUES7 * YEAR Crosstabulation
YEAR
Total
2003
2004
2005
2006
QUES7
1
Count
143
87
42
10
282
Expected Count
132.7
83.7
49.4
16.1
282.0
2
Count
120
79
56
22
277
Expected Count
130.3
82.3
48.6
15.9
277.0
Total
Count
263
166
98
32
559
Expected Count
263.0
166.0
98.0
32.0
559.0
ChiSquare Tests
0 cells (.0%) have expected count less than 5. The minimum expected count is 15.86.
Value
df
Asymp. Sig. (2sided)
Pearson ChiSquare
8.853
____ ____ N of Valid Cases
559
(For this question, an answer of 1 indicates that the student has heard of SJC, while a 2 indicates they the student has not heard of SJC. Year represents year of graduation, so 2003 is a senior and 2006 is a freshman.)
The degrees of freedom are 3.
The level of significance is .031
a) 263*282/559
b) The percentage of students who have heard of the college
declines as they get further away from graduation. So, yes,
eyeballing the data suggests the researcher's suspicion may
be correct. However, it is not clear if the trend is strong
enough to be more than random.
c) The claim or null hypothesis, which we want to show is
incorrect, is that year in school has no impact on whether
students have heard of the college. The alternative is that
the year in school matters.
d) (143137.2)^{2}/137.2 + (120 
130.3)^{2}/130.3 + etc.
e) 3. (number of row 1)*(number of columns  1) = 1*3 =
3
f) You would reject the claim that the results are random
and say that the results show that year in school influences
how aware the students are of the college.
g) You would say that the evidence is not strong enough to
reject the claim that the year of students matters in their
awareness of the college.
3. A political candidate has a survey done to determine how popular he is with various groups. He finds the following:
Age: Preference:
over 65 under 65 Total support him
18 12 30 oppose him
22 48 70 Total
40 60 100


Preference: 



support him 



oppose him 



Total 



a) Missing numbers in the
first row: 12, 18. In the second row: 28, 42.
b) 1. (21)*)21) = 1.
c) 3.84, found in a table.
d) 6.64.
e) 7.143
f) Reject the claim that age does not matter. The
probability that we get a result like this by random chance
if there are no differences by age is only
.00752.
4. A statistics professor believes that students in his morning classes do better than students in his afternoon classes. His department chairman says the differences are random and that students do equally well regardless of time. The professor finds his grades for the past semesters and finds the following:
Letter Grade: Time the Classes Met:
A B C D F Total Morning
12 18 13 11 6 60 Afternoon
3 7 17 4 9 40 Total
15 25 30 15 15 100
Using the Chisquare test, do you conclude that the morning classes and afternoon classes were somehow different?
The Chisquare statistic is 11.083 with 4 degrees of freedom. The pvalue or level of significance is .02564. If we want just strong evidence, setting our cutoff level of significance at .05, then the evidence is enough to conclude that the morning classes are different from the afternoon classes. However, if we wanted overwhelming evidence, setting the cutoff level of significance at .01, then this evidence is still not enough to reject the claim that there is no real difference in the classes. By random chance we would get a result this far from the expected values about 2.5% of the time.