Question

4. Suppose a researcher is analyzing the relationship between gender and favorite type of movie out of drama, science fiction and comedy. Here is the data using a random sample: Drama Science Fiction Comedy Total Male 28 152 218 398 Female 213 102 189 504 Total 241 254 407 902 Test whether gender and type of favorite movie are independent at the .05 level of significance. Show all five steps of this test.

Answer 1

. Step 1: Create a Contingency table for the above problem:

	Drama	Science Fiction	Comedy	Total
Male	28	152	218	398
Female	213	102	189	504
Total	241	254	407	902

Here We have to test whether gender & type of favourite movie are independent or not?

So, We can apply Chi-Square χ2 independence of attribute test.

Step 2: Define a level of significance α = 0.05.

Step 3: Calculate the Expected value for each observation.

Step 4: Calculated test statistic  χ2 = 142.08 which follow (3-1)*(2-1)= 2*1=2 degree of freedom

Step 5: The tabulated value of χ2 at 2 degrees of freedom= 5.991

Conclusion: Since the calculated value of χ2 is greater than the tabulated value of χ2. So, we will reject the Null Hypothesis (H0) & hence we can conclude that types of favourite Movie depend upon the gender.