262 WordsJan 28, 20132 Pages

Chi –Square Distribution to test the independence of two variables
Step 1: Set up the hypotheses:
Hº: The variables are independent H¹: The variables are not independent.
Step 2: Compute the expected frequency for each cell in the contingency table by use of the formula:
E=Expected frequency= (Row total)(Column Total) _____________________ Sample size
Step 3: Compute the statistic χ ²=Σ(O-E)² / E Where O is the observed frequency, E is the expected frequency, and the sum Σ is over all cells.
Step 4: Find the critical value χ²α in Table A. 10 page 651. Use the level of significance of 0.01 and the number of degrees of freedom. d.f. to find the critical value. d.f.= (R-1)(C-1)
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where R is the number of rows and C is the number of columns of cells in the contingency table. The critical region consists of all values of χ²α.
Step5: Compare the sample statistic χ² of Step 3 with the critical value of χ²α of Step 4. If the sample statistic is larger, reject the null hypothesis of independence. Otherwise, do not reject the null hypothesis.
Problem
The following table shows the Myers-Briggs personality preference and professions for a random sample of 2408 people in the listed professions.
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