A researcher is interested in whether or not domestic violence occurs in the same proportion in families of alcoholics as it does in the population in general.If the relative frequency of domestic violence in the population is .05 and the relative frequency of no domestic violence in the population is .95,what is the chi-square goodness-of-fit value for the following data?

A)5.5
B)21.23
C)30
D)60.5

Question

A researcher is interested in whether or not domestic violence occurs in the same proportion in families of alcoholics as it does in the population in general.If the relative frequency of domestic violence in the population is .05 and the relative frequency of no domestic violence in the population is .95,what is the chi-square goodness-of-fit value for the following data?

A)5.5 
B)21.23 
C)30 
D)60.5

Quizplus · Accepted Answer

We can use the chi-square goodness-of-fit formula:

χ^2 = Σ[(Observed frequency - Expected frequency)^2 / Expected frequency]

We can calculate the expected frequency for domestic violence as:

Expected frequency = Total sample size * Relative frequency of domestic violence in the population
Expected frequency = 100 * 0.05
Expected frequency = 5

We can calculate the expected frequency for no domestic violence as:

Expected frequency = Total sample size * Relative frequency of no domestic violence in the population
Expected frequency = 100 * 0.95
Expected frequency = 95

We can then calculate the chi-square goodness-of-fit value:

χ^2 = [(10-5)^2/5] + [(90-95)^2/95]
χ^2 = 5 + 0.263
χ^2 = 5.263

Looking at the answer choices, the closest value to 5.263 is B) 21.23, so that is our answer.

A Researcher Is Interested in Whether or Not Domestic Violence