A study was conducted to determine whether the use of seat b

A study was conducted to determine whether the use of seat belts in motor vehicles depends on the educational status of the parents. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) parents\' educational status (College Degree or Non-College Degree) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table.

Non college degree college degree

Seat belts not worn 31 148

Seat belts worn 283 330

At 5% level of significance, what is the critical value of the test statistic rounded to four decimal places?

Solution

A study was conducted to determine whether the use of seat belts in motor vehicles depends on the educational status of the parents. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) parents\' educational status (College Degree or Non-College Degree) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table.

College degree Non college degree

Seat belts not worn 31 148

Seat belts worn 283 330

At 5% level of significance, what is the critical value of the test statistic rounded to four decimal places?

Answer

2 rows and 2 columns

Degress of freedom = (2-1)*(2-1) =1

critical value = 3.8415

calculated test statistic = 48.1849 > 3.8415 the table value at 0.05 level.

The null hypothesis is rejected

We conclude that the use of seat belts in motor vehicles depends on the educational status of the parents.

Chi-Square Test

Observed Frequencies

Column variable

Calculations

Row variable

C1

C2

Total

fo-fe

R1

31

148

179

-39.9672

39.9672

R2

283

330

613

39.9672

-39.9672

Total

314

478

792

Expected Frequencies

Column variable

Row variable

C1

C2

Total

(fo-fe)^2/fe

R1

70.9672

108.0328

179

22.5086

14.7860

R2

243.0328

369.9672

613

6.5727

4.3176

Total

314

478

792

Data

Level of Significance

0.05

Number of Rows

2

Number of Columns

2

Degrees of Freedom

1

Results

Critical Value

3.8415

Chi-Square Test Statistic

48.1849

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
Row variable	C1	C2	Total		fo-fe
R1	31	148	179		-39.9672	39.9672
R2	283	330	613		39.9672	-39.9672
Total	314	478	792
Expected Frequencies
	Column variable
Row variable	C1	C2	Total		(fo-fe)^2/fe
R1	70.9672	108.0328	179		22.5086	14.7860
R2	243.0328	369.9672	613		6.5727	4.3176
Total	314	478	792
Data
Level of Significance	0.05
Number of Rows	2
Number of Columns	2
Degrees of Freedom	1
Results
Critical Value	3.8415
Chi-Square Test Statistic	48.1849