Fifty fifth-grade students from each of four city schools were given a standardi
ID: 3156116 • Letter: F
Question
Fifty fifth-grade students from each of four city schools were given a standardized fifth-grade reading test. After grading, each student was rated as satisfactory or not satisfactory in reading ability, with the following results:
Each number represent number of unsatisfactory students in each city school. 7, 10, 13, 6.
Is there sufficient evidence to indicate that the percentage of fifth-grade students with an unsatisfactory reading ability varies from school to school? Use 1% level of significance level.
Solution:
At least one proportion differs from at least one another. Test statistics: ______
Degree of freedom: 3
Critical value: _______
Therefore, we can/ cannot ? reject the null hypothesis that reading ability for the fifth-grades as measured by this test does not vary from school to school.
Explanation / Answer
Fifty fifth-grade students from each of four city schools were given a standardized fifth-grade reading test. After grading, each student was rated as satisfactory or not satisfactory in reading ability, with the following results:
Each number represent number of unsatisfactory students in each city school. 7, 10, 13, 6.
Is there sufficient evidence to indicate that the percentage of fifth-grade students with an unsatisfactory reading ability varies from school to school? Use 1% level of significance level.
Solution:
At least one proportion differs from at least one another. Test statistics: 4.065
Degree of freedom: 3
Critical value: 11.345
Therefore, we cannot reject the null hypothesis that reading ability for the fifth-grades as measured by this test does not vary from school to school.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
C4
Total
fo-fe
R1
7
10
13
6
36
-2
1
4
-3
R2
43
40
37
44
164
2
-1
-4
3
Total
50
50
50
50
200
Expected Frequencies
Column variable
Row variable
C1
C2
C3
C4
Total
(fo-fe)^2/fe
R1
9
9
9
9
36
0.4444
0.1111
1.7778
1.0000
R2
41
41
41
41
164
0.0976
0.0244
0.3902
0.2195
Total
50
50
50
50
200
Data
Level of Significance
0.01
Number of Rows
2
Number of Columns
4
Degrees of Freedom
3
Results
Critical Value
11.345
Chi-Square Test Statistic
4.0650
p-Value
0.2545
Do not reject the null hypothesis
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
C4
Total
fo-fe
R1
7
10
13
6
36
-2
1
4
-3
R2
43
40
37
44
164
2
-1
-4
3
Total
50
50
50
50
200
Expected Frequencies
Column variable
Row variable
C1
C2
C3
C4
Total
(fo-fe)^2/fe
R1
9
9
9
9
36
0.4444
0.1111
1.7778
1.0000
R2
41
41
41
41
164
0.0976
0.0244
0.3902
0.2195
Total
50
50
50
50
200
Data
Level of Significance
0.01
Number of Rows
2
Number of Columns
4
Degrees of Freedom
3
Results
Critical Value
11.345
Chi-Square Test Statistic
4.0650
p-Value
0.2545
Do not reject the null hypothesis
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