Discuss the below:
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:
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 .Use the level of significance of 0.01 and the number of degrees of d.f. to find the critical value.
d.f.= (R-1)(C-1)
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.
Q: The following table shows the Myers-Briggs personality preference and professions for a random sample of 2408 people in the listed professions.
Personality Preference Type
Occupation Extrovert Introvert Row Total
_Clergy_____________________________________308_____________226________534__
_M.D._______________________667________936______ _1603_ Lawyer_______________________112________159________271____Column total___________________ 1087_____- 1321 2408 _
Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.01 level of significance.