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: 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:  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

We can perform a chi-square test of independence to determine if the observed frequencies in the table are significantly different from what we would expect if the prime rate and inflation were independent. Using a significance level of .01 and the degrees of freedom (df) = (3-1)(5-1) = 8, we obtain a critical chi-square value of 21.955. Calculating the test statistic using the formula chi-square = Σ [(O-E)^2/E], we find a value of 44.72. This exceeds the critical value, so we reject the null hypothesis that the prime rate and inflation are independent. Therefore, the best conclusion is that the prime rate and inflation rate are not independent (option B). The fact that some cells have small observed frequencies does not invalidate this conclusion, as long as the overall test is significant. Option C can therefore be ruled out. Option D is also not correct, as there are no expected frequencies of 5 or less in any cell, so this is not a concern for the validity of the chi-square test.

You Want to Test the Hypothesis That the Prime Rate