Recent studies have found that American children are more ob

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?

Solution

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