Recent studies have found that American children are more obese than in the past
ID: 3437028 • Letter: R
Question
Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the mean number of hours spent watching TV and weights are independent at 1% level of significance.
Weights Tv Hours Total
0-3 3-6 6+
More than 10Ibs overweight 1 9 20
Within than 10lbs of normal weight 20 15 15
More than 10lbs underweight 10 5 5
Total 31 29 40
What is the degrees of freedom of the test statistic?
Explanation / Answer
Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the mean number of hours spent watching TV and weights are independent at 1% level of significance.
Weights Tv Hours Total
0-3 3-6 6+
More than 10Ibs overweight 1 9 20
Within than 10lbs of normal weight 20 15 15
More than 10lbs underweight 10 5 5
Total 31 29 40
What is the degrees of freedom of the test statistic =4
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
Total
fo-fe
R1
1
9
20
30
-8.3
0.3
8
R2
20
15
15
50
4.5
0.5
-5
R3
10
5
5
20
3.8
-0.8
-3
Total
31
29
40
100
Expected Frequencies
Column variable
Row variable
C1
C2
C3
Total
(fo-fe)^2/fe
R1
9.3
8.7
12
30
7.4075
0.0103
5.3333
R2
15.5
14.5
20
50
1.3065
0.0172
1.2500
R3
6.2
5.8
8
20
2.3290
0.1103
1.1250
Total
31
29
40
100
Data
Level of Significance
0.01
Number of Rows
3
Number of Columns
3
Degrees of Freedom
4
Results
Critical Value
13.2767
Chi-Square Test Statistic
18.8893
Calculated chi square value 18.8893 > 13.2767 the table value
The null hypothesis is rejected.
We conclude that the mean number of hours spent watching TV and weights are not independent at 1% level of significance.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
Total
fo-fe
R1
1
9
20
30
-8.3
0.3
8
R2
20
15
15
50
4.5
0.5
-5
R3
10
5
5
20
3.8
-0.8
-3
Total
31
29
40
100
Expected Frequencies
Column variable
Row variable
C1
C2
C3
Total
(fo-fe)^2/fe
R1
9.3
8.7
12
30
7.4075
0.0103
5.3333
R2
15.5
14.5
20
50
1.3065
0.0172
1.2500
R3
6.2
5.8
8
20
2.3290
0.1103
1.1250
Total
31
29
40
100
Data
Level of Significance
0.01
Number of Rows
3
Number of Columns
3
Degrees of Freedom
4
Results
Critical Value
13.2767
Chi-Square Test Statistic
18.8893
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