Question

The table below summarizes data from a survey of a sample of women. Using a 0.05 significance​ level, and assuming that the sample sizes of 900 men and 400 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?

   Man   Woman
Women who agree   605   322
Women who disagree   295   78

Identify the null and alternative hypotheses. Choose the correct answer below.

A.

Upper H 0H0​:

The proportions of​ agree/disagree responses are the same for the subjects interviewed by men and the subjects interviewed by women.

Upper H 1H1​:

The proportions are different.

B.

Upper H 0H0​:

The response of the subject and the gender of the subject are independent.

Upper H 1H1​:

The response of the subject and the gender of the subject are dependent.

C.

Upper H 0H0​:

The proportions of​ agree/disagree responses are different for the subjects interviewed by men and the subjects interviewed by women.

Upper H 1H1​:

The proportions are the same.

Compute the test statistic.

nothing

​(Round to three decimal places as​ needed.)

Find the critical​ value(s).

nothing

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

What is the conclusion based on the hypothesis​ test?

▼

Reject

Fail to reject

  

Upper H 0H0.

There

▼

is

is not

sufficient evidence to warrant rejection of the claim that the proportions of​ agree/disagree responses are the same for subjects interviewed by men and the subjects interviewed by women. It

▼

does not appear

appears

that the gender of the interviewer affected the responses of women.

Click to select your answer(s).

Answer 1

(a)
Correct option:

A. H0: The proportions of​ agree/disagree responses are the same for subjects interviewed by men and the subjects interviewed by women.

         H1: The proportions are different

(b)

Observed Frequencies:

	Men	Women	Total
Women who agree	605	322	927
Women who disagree	295	78	373
Total	900	400	1300

Expected Frequencies:

	Men	Women	Total
Women who agree	900X927/133=641.7692	400X927/1300=285.2308	927
Women who disagree	900X373/1300=258.2308	400X373/1300=114.7692	373
Total	900	400	1300

Test Statistic is got as follows:

Observed (O)	Expected (E)	(O - E)2/E
605	641.7692	2.1066
322	285.2308	4.7399
295	258.2308	5.2355
78	114.7692	11.7799
Total = =		23.862

Test statistic is:23.862

(c)

= 0.05

ndf = (r - 1) X (c - 1)

= ( 2 - 1) X (2 - 1)

= 1

From Table, critical value of = 3.842

(d)

Correct option:

Reject H0

(e)

There is sufficient evidence to to warrant rejection of the claim that the proportions of​ agree/disagree responses are the same for subjects interviewed by men and the subjects interviewed by women.

(f)

It appears that gender of the interviewer affected the responses of women.