1. A recent baseball IQ test was given to 250 random Connecticut baseball fans.
ID: 3364435 • Letter: 1
Question
1. A recent baseball IQ test was given to 250 random Connecticut baseball fans. The scores were classified as Low (little or no baseball knowledge), Intermediate (moderate baseball knowledge) and High (substantial baseball knowledge). Subjects also indicated their favorite baseball team (Mets, Red Sox or Yankees). The results are given in the table below. (Note that since all cells had to have a minimum of 5 to use the test, the last cell had to be augmented by 3)
a. Test the claim that IQ score classification and Favorite team are associated. Be sure to state the null and alternative hypotheses, the test statistic, p-value, and conclusion in plain English. Include the table of expected frequencies.
b. Find the probabilities that a fan scored High given he/she was a fan of each team. (There are 3 probabilities to calculate here).
c. Find the probabilities that a fan scored Low given he/she was a fan of each team. (There are 3 probabilities to calculate here).
d. Write one or two sentences summarizing your findings.
Round answers to the thousandths place.
Score Intermediate 12 48 13 High 38 Low Team Mets Red Sox Yankees 20 85 5Explanation / Answer
Result:
Ho: there is no association between IQ score classification and Favorite team
H1: there is a association between IQ score classification and Favorite team
test statistic= 139.410
p-value= 0.0000
since P value < 0.05, Ho is rejected.
We conclude that there is association between IQ score classification and Favorite team.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
Total
fo-fe
R1
7
12
38
57
-18.5360
-4.6440
23.1800
R2
20
48
22
90
-20.3200
21.7200
-1.4000
R3
85
13
5
103
38.8560
-17.0760
-21.7800
Total
112
73
65
250
Expected Frequencies
Column variable
Row variable
C1
C2
C3
Total
(fo-fe)^2/fe
R1
25.536
16.644
14.82
57
13.4549
1.2958
36.2559
R2
40.32
26.28
23.4
90
10.2406
17.9512
0.0838
R3
46.144
30.076
26.78
103
32.7191
9.6951
17.7135
Total
112
73
65
250
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
3
Degrees of Freedom
4
Results
Critical Value
9.488
Chi-Square Test Statistic
139.4099
p-Value
0.0000
Reject the null hypothesis
mets
0.667
Red sox
0.244
yankees
0.049
mets
0.123
Red sox
0.222
yankees
0.825
d. Write one or two sentences summarizing your findings.
We conclude that there is association between IQ score classification and Favorite team.
Probabilities that a fan scored high given he/she was a fan of mets team is 0.667.
Probabilities that a fan scored Low given he/she was a fan of yankees team is 0.825
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
Total
fo-fe
R1
7
12
38
57
-18.5360
-4.6440
23.1800
R2
20
48
22
90
-20.3200
21.7200
-1.4000
R3
85
13
5
103
38.8560
-17.0760
-21.7800
Total
112
73
65
250
Expected Frequencies
Column variable
Row variable
C1
C2
C3
Total
(fo-fe)^2/fe
R1
25.536
16.644
14.82
57
13.4549
1.2958
36.2559
R2
40.32
26.28
23.4
90
10.2406
17.9512
0.0838
R3
46.144
30.076
26.78
103
32.7191
9.6951
17.7135
Total
112
73
65
250
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
3
Degrees of Freedom
4
Results
Critical Value
9.488
Chi-Square Test Statistic
139.4099
p-Value
0.0000
Reject the null hypothesis
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