The table lists the number of students from three different high schools partici
ID: 3436791 • Letter: T
Question
The table lists the number of students from three different high schools participating in the mathematics and physics sections of a science fair. At = 0.05, test the claim that the section of participation and the high school where the students were from are independent.
Number of Students
Each separate number represents school 1, 2, and 3
Mathematics 7, 10, 16
Physics 28, 15, 25
A. There is evidence to reject the claim that the high school and the section of participation are independent because the test value 12.592 > 1.198
B. There is no evidence to reject the claim that the high school and the section of participation are independent because the test value 1.198 < 5.991
C. There is evidence to reject the claim that the high school and the section of participation are independent because the test value 5.991 > 1.198
D. There is no evidence to reject the claim that the high school and the section of participation are independent because the test value 3.917 < 5.991
Explanation / Answer
The table lists the number of students from three different high schools participating in the mathematics and physics sections of a science fair. At = 0.05, test the claim that the section of participation and the high school where the students were from are independent.
Number of Students
Each separate number represents school 1, 2, and 3
Mathematics 7, 10, 16
Physics 28, 15, 25
A. There is evidence to reject the claim that the high school and the section of participation are independent because the test value 12.592 > 1.198
B. There is no evidence to reject the claim that the high school and the section of participation are independent because the test value 1.198 < 5.991
C. There is evidence to reject the claim that the high school and the section of participation are independent because the test value 5.991 > 1.198
D. There is no evidence to reject the claim that the high school and the section of participation are independent because the test value 3.917 < 5.991
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
Total
fo-fe
R1
7
10
16
33
-4.4356
1.8317
2.6040
R2
28
15
25
68
4.4356
-1.8317
-2.6040
Total
35
25
41
101
Expected Frequencies
Column variable
Row variable
C1
C2
C3
Total
(fo-fe)^2/fe
R1
11.4356
8.1683
13.3960
33
1.7205
0.4107
0.5062
R2
23.5644
16.8317
27.6040
68
0.8349
0.1993
0.2456
Total
35
25
41
101
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
5.991
Chi-Square Test Statistic
3.917
p-Value
0.1410
Do not reject the null hypothesis
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
Total
fo-fe
R1
7
10
16
33
-4.4356
1.8317
2.6040
R2
28
15
25
68
4.4356
-1.8317
-2.6040
Total
35
25
41
101
Expected Frequencies
Column variable
Row variable
C1
C2
C3
Total
(fo-fe)^2/fe
R1
11.4356
8.1683
13.3960
33
1.7205
0.4107
0.5062
R2
23.5644
16.8317
27.6040
68
0.8349
0.1993
0.2456
Total
35
25
41
101
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
5.991
Chi-Square Test Statistic
3.917
p-Value
0.1410
Do not reject the null hypothesis
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