Students were sampled to determine their support for the legalization of gambling in their community. A sample of 150 students were asked whether or not they supported legalization of gambling,and the following results were obtained. The value of the chi-square test statistic equals ________.
A)−3
B)−2
C)+3

Question

Students were sampled to determine their support for the legalization of gambling in their community. A sample of 150 students were asked whether or not they supported legalization of gambling,and the following results were obtained.  The value of the chi-square test statistic equals ________.
A)−3 
B)−2 
C)+3

Quizplus · Accepted Answer

The chi-square test statistic cannot be negative, so we can eliminate choices A and B. To calculate the chi-square test statistic, we need to compare the observed frequencies to the expected frequencies under the assumption that there is no association between support for legalization of gambling and being a student. If we calculate the expected frequencies, we can use the formula: (row total x column total) / grand total. The grand total is 150, the row totals are 91 and 59, and the column totals are 102 and 48. Using these values, we get an expected frequency of 50.84 for those who support legalization and are students, and an expected frequency of 8.16 for those who oppose legalization and are not students. We can then calculate the chi-square test statistic using the formula: sum of (observed frequency - expected frequency)^2 / expected frequency. When we plug in the observed and expected frequencies, we get a chi-square test statistic of 4. Thus, the correct answer is D.

Students Were Sampled to Determine Their Support for the Legalization