The table below summarizes data trom a survey of a sample of women. Using a 0.05
ID: 2908670 • Letter: T
Question
The table below summarizes data trom a survey of a sample of women. Using a 0.05 significance level, and assurning that the sample sizes of 700 men and 300 women are predetermined, test the claim that the proportions of agree/disagree responses are the same for subjects interviewed by men and the subjects interviewed by women. Does it appear that the gender of the interviewer affected the responses of women? Gender of Interviewer Man 424 276 Woman 250 50 Women who agree Women who disagree Identify the null and alternative hypotheses. Choose the correct answer below O A. Ho: The response of the subject and the gender of the subject are independent O B. Ho: The proportions of agree/disagree responses are the same for the subjects interviewed by men and the subjects interviewed by women ? ?· Mo: The proportions of agreed agree responses are different for the sub ects interviewed by men and the sub ects nterviewed by wor en H The response of the subject and the gender of the subject are dependent H, The proportions are different H: The proportions are the same.Explanation / Answer
Solution:
Here, we have to use chi square test for independence of two categorical variables. The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: The response of the subject and the gender of the subject are independent.
Alternative hypothesis: Ha: The response of the subject and the gender of the subject are dependent.
(Correct answer: A)
We are given
Level of significance = ? = 0.05
Test statistic formula is given as below:
Chi square = ?[(O – E)^2/E]
Where, O is the observed frequencies and E is expected frequencies.
Calculation tables are given as below:
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
Men
Women
Total
(O - E)
Agree
424
250
674
-47.8
47.8
Disagree
276
50
326
47.8
-47.8
Total
700
300
1000
Expected Frequencies
Column variable
Row variable
Men
Women
Total
(O - E)^2/E
Agree
471.8
202.2
674
4.842815
11.2999
Disagree
228.2
97.8
326
10.01245
23.36237
Total
700
300
1000
Chi square = ?[(O – E)^2/E] = 49.51753
Number of rows = r = 2
Number of columns = c = 2
Degrees of freedom = (r – 1)*(c – 1)
Degrees of freedom = (2 – 1)*(2 – 1)
Degrees of freedom = 1*1 = 1
Critical value = 3.841459
P-value = 0.0000
(Critical value and P-value is calculated by using Ti-84 calculator. In Ti-84 calculator, press 2nd > VARS to get the DISTR menu. Scroll down to Chi square and select pdf/cdf/inv function according to find critical/P-value and press enter. Enter the values of Chi square statistic and degrees of freedom.)
? = 0.05
P-value < ? = 0.05
So, we reject the null hypothesis that the response of the subject and the gender of the subject are independent.
There is sufficient evidence to conclude that the response of the subject and the gender of the subject are dependent.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
Men
Women
Total
(O - E)
Agree
424
250
674
-47.8
47.8
Disagree
276
50
326
47.8
-47.8
Total
700
300
1000
Expected Frequencies
Column variable
Row variable
Men
Women
Total
(O - E)^2/E
Agree
471.8
202.2
674
4.842815
11.2999
Disagree
228.2
97.8
326
10.01245
23.36237
Total
700
300
1000
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