A study was conducted to determine whether the use of seat belts in motor vehicl
ID: 3437005 • Letter: A
Question
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
What is the calculated test statistic, rounded to four decimal places?
Explanation / Answer
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
What is the calculated test statistic, rounded to four decimal places?
calculated test statistic = 48.1849
calculated test statistic = 48.1849 > 3.841 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
3.841
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
3.841
Chi-Square Test Statistic
48.1849
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