Question

Please show how to answer using TI 84 caculator. The question ask to compute the test statistic and find the critical value. Thank you.

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.

Answer 1

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: H_a: 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 2^nd > 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.