The table lists the number of students from three different

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

Solution

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