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 700 men and 300 women are​ predetermined, test the claim...


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 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


Woman






Women who agree




487


235






Women who disagree




213


65


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






A.



H0​:

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


H1​:

The proportions are different.






B.



H0​:

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


H1​:

The proportions are the same.






C.



H0​:

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


H1​:

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



Determine the test statistic.

χ2=



Determine the​ P-value of the test statistic.

​P-value=



Do the results suggest that polygraphs are effective in distinguishing between truth and​ lies?




A.



There is not

sufficient evidence to warrant rejection of the claim that polygraph testing is​ 95% accurate.






B.



There is not

sufficient evidence to warrant rejection of the claim that whether a subject lies is independent of the polygraph test indication.










C.



There is

sufficient evidence to warrant rejection of the claim that polygraph testing is​ 95% accurate.






D.



There is

sufficient evidence to warrant rejection of the claim that whether a subject lies is independent of the polygraph test indication.







Jun 08, 2022
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