Question

Conduct a statistical test at a significance level of 0.05 to determine if there is an association between gender and movie preference. The chart of observed counts has been re-copied here for convenience. Male Female Total Action 52 24 76 Drama 32 32 64 Comedy 20 16 36 Animated 16 8 24 Total 120 80 200 Answer in the blanks to show the work associated with exploring this claim. Blank #1: The statistical test to determine whether there is an association between two categorical variables is the ___overall relationship test. Blank #2: Compute the expected count of Females who prefer comedy. Report your answer with one decimal place. The test was conducted and the following test statistic and p-value calculated as shown in the calculator screenshot. Fill in the remaining blanks to show the test in its entirety. X2-Test X2=5. 1442 p=.129 df 3 Blank #3: Ho: There is not) an association between gender and movie preference. (is or Blank #4:

Answer 1

1)

Chi square of independence

2)

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	action	drama	comedy	animated			Total
Male	76*120/200=45.6	64*120/200=38.4	36*120/200=21.6	24*120/200=14.4			120
Female	76*80/200=30.4	64*80/200=25.6	36*80/200=14.4	24*80/200=9.6			80

(fo-fe)^2/fe	action	drama	comedy	animated
Male	0.898	1.067	0.119	0.178
Female	1.347	1.600	0.178	0.267

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   5.653
  
Level of Significance =   0.05
Number of Rows =   2
Number of Columns =   4
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 4- 1 ) =   3
  
p-Value =   0.130

3)

There is no association

4)

There is association

5)

Decision:    p value > α , do not reject Ho

6)

does not favor

Please let me know in case of any doubt.

Thanks in advance!

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