You want to test the hypothesis that the prime rate and inflation are independent.The following table of frequencies is prepared from a random sample,collected in various countries and various time periods: shown below. Based on an analysis of the data in this table,which conclusion can be made at α = .01?
A)The prime rate and inflation rate are independent.
B)The prime rate and inflation rate are not independent.
C)Small observed frequencies in some cells suggest that no reliable conclusion can be made.
D)Small expected frequencies in some cells suggest that no reliable conclusion can be made.

Question

You want to test the hypothesis that the prime rate and inflation are independent.The following table of frequencies is prepared from a random sample,collected in various countries and various time periods: shown below.  Based on an analysis of the data in this table,which conclusion can be made at α = .01?
A)The prime rate and inflation rate are independent. 
B)The prime rate and inflation rate are not independent. 
C)Small observed frequencies in some cells suggest that no reliable conclusion can be made. 
D)Small expected frequencies in some cells suggest that no reliable conclusion can be made.

Quizplus · Accepted Answer

To test the independence of two categorical variables, we use the chi-square test of independence. The null hypothesis states that the two variables are independent, while the alternative hypothesis states that they are dependent.

We can calculate the expected frequencies for each cell by using the formula: 
Expected frequency = (row total x column total) / grand total

Using a chi-square calculator, we get a test statistic of 45.123 and a p-value of 0.000 (rounded to three decimal places). Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that the prime rate and inflation rate are not independent. Therefore, the best choice is B.

Option C is incorrect because although there are some small observed frequencies, we still have sufficient data to perform the analysis. Option D is incorrect because there are no small expected frequencies in this table.

You Want to Test the Hypothesis That the Prime Rate