The contingency table shows how a random sample of colle ge freshmen graded the
ID: 3318910 • Letter: T
Question
The contingency table shows how a random sample of colle ge freshmen graded the leaders of three types of institutions. At : 0.10, can y (a) Identifty the claim and state the null and alternative hypotheses Ho: Grades are independent of the institution. Ha: Grades are dependent on the institution The alternative hypothesis is the claim. (b) Determine the degrees of freedom, find the critical value, and identify the rejection region. What are the degrees of freedom? Find the critical value. (Round to three decimal places as needed.)Explanation / Answer
Result:
Df=6
Critical chi square =10.645
Reject Ho if calculated chi square > 10.645.
Calculated chi square =19.750, Ho is rejected.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
A
B
C
D
Total
fo-fe
Military
31
49
25
17
122
8.7840
1.9321
-7.7593
-2.9568
Religious
16
47
23
15
101
-2.3920
8.0340
-4.1204
-1.5216
Media
12
29
39
21
101
-6.3920
-9.9660
11.8796
4.4784
Total
59
125
87
53
324
Expected Frequencies
Column variable
0
A
B
C
D
Total
(fo-fe)^2/fe
Military
22.2160
47.0679
32.7593
19.9568
122
3.4731
0.0793
1.8378
0.4381
Religious
18.3920
38.9660
27.1204
16.5216
101
0.3111
1.6564
0.6260
0.1401
Media
18.3920
38.9660
27.1204
16.5216
101
2.2215
2.5489
5.2037
1.2139
Total
59
125
87
53
324
Data
Level of Significance
0.10
Number of Rows
3
Number of Columns
4
Degrees of Freedom
6
Results
Critical Value
10.645
Chi-Square Test Statistic
19.7500
p-Value
0.0031
Reject the null hypothesis
Chi-Square Test
Observed Frequencies
Column variable
Calculations
A
B
C
D
Total
fo-fe
Military
31
49
25
17
122
8.7840
1.9321
-7.7593
-2.9568
Religious
16
47
23
15
101
-2.3920
8.0340
-4.1204
-1.5216
Media
12
29
39
21
101
-6.3920
-9.9660
11.8796
4.4784
Total
59
125
87
53
324
Expected Frequencies
Column variable
0
A
B
C
D
Total
(fo-fe)^2/fe
Military
22.2160
47.0679
32.7593
19.9568
122
3.4731
0.0793
1.8378
0.4381
Religious
18.3920
38.9660
27.1204
16.5216
101
0.3111
1.6564
0.6260
0.1401
Media
18.3920
38.9660
27.1204
16.5216
101
2.2215
2.5489
5.2037
1.2139
Total
59
125
87
53
324
Data
Level of Significance
0.10
Number of Rows
3
Number of Columns
4
Degrees of Freedom
6
Results
Critical Value
10.645
Chi-Square Test Statistic
19.7500
p-Value
0.0031
Reject the null hypothesis
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