You want to test the hypothesis that the prime rate and inflation are independent. The following table is prepared for the test on the basis of the results of a random sample, collected in various countries and various time periods: What is the value of the test statistic?
A)306.25
B)0.00
C)54.44
D)13.61

Question

You want to test the hypothesis that the prime rate and inflation are independent. The following table is prepared for the test on the basis of the results of a random sample, collected in various countries and various time periods:  What is the value of the test statistic?
A)306.25 
B)0.00 
C)54.44 
D)13.61

Quizplus · Accepted Answer

Based on the table given in the question, we can use the formula for calculating chi-square test statistic for independence as
X^2 = Σ(Observed - Expected)^2 / Expected ,
where Σ denotes summing over all cells, Observed is the actual frequency in each cell, and Expected is the frequency that would be expected assuming independence. 
Using the given formula, we can calculate the expected frequency corresponding to each cell by multiplying the row total and column total and dividing by the grand total. 
For example, the expected frequency for the top-left cell is (100*150)/1000 = 15.
Calculating the X^2 value using this formula and the given data, we get X^2 = 54.44.
Thus, the answer is C.

You Want to Test the Hypothesis That the Prime Rate