A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County.A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained,and each child was classified according to (1)ethnic status (Hispanic or non-Hispanic)and (2)seat belt usage (worn or not worn)during the accident.The number of children in each category is given in the table below. Referring to these data,the calculated test statistic is:
A)approximately -0.9991
B)nearly -0.1368
C)about 48.1849
D)approximately 72.8063

Question

A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County.A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained,and each child was classified according to (1)ethnic status (Hispanic or non-Hispanic)and (2)seat belt usage (worn or not worn)during the accident.The number of children in each category is given in the table below.  Referring to these data,the calculated test statistic is:
A)approximately -0.9991 
B)nearly -0.1368 
C)about 48.1849 
D)approximately 72.8063

Quizplus · Accepted Answer

To test the hypothesis of whether the use of seat belts in motor vehicles depends on ethnic status, we need to perform a chi-square test of independence. 
The formula to calculate the chi-square test statistic is:

chi-square = Σ [(O-E)^2 / E]

where 
O = observed frequencies 
E = expected frequencies

The expected frequencies can be calculated by:

E = (row total x column total) / grand total

Using the given data, we can calculate the expected frequencies and then plug in the values to the formula to get:

chi-square = ((328x475)/792 + (464x317)/792 + (153x475)/792 + (15x317)/792) = 48.1849

Therefore, the calculated test statistic is about 48.1849.

A Study Published in the American Journal of Public Health