11.2,1 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 400 women are​ predetermined, test the...



 11.2,1





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
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?





























































Gender of Interviewer










Man


Woman






Women who agree




458


345






Women who disagree




242


55







Chi Square distribution below;




Area to the Right of the Critical Value



















































































































































Degrees of Freedom


0.995


0.99


0.975


0.95


0.90


0.10


0.05


0.025


0.01


0.005


1


​-


​-


0.001


0.004


0.016


2.706


3.841


5.024


6.635


7.879


2


0.010


0.020


0.051


0.103


0.211


4.605


5.991


7.378


9.210


10.597


3


0.072


0.115


0.216


0.352


0.584


6.251


7.815


9.348


11.345


12.838


4


0.207


0.297


0.484


0.711


1.064


7.779


9.488


11.143


13.277


14.860


5


0.412


0.554


0.831


1.145


1.610


9.236


11.071


12.833


15.086


16.750


6


0.676


0.872


1.237


1.635


2.204


10.645


12.592


14.449


16.812


18.548


7


0.989


1.239


1.690


2.167


2.833


12.017


14.067


16.013


18.475


20.278


8


1.344


1.646


2.180


2.733


3.490


13.362


15.507


17.535


20.090


21.955


9


1.735


2.088


2.700


3.325


4.168


14.684


16.919


19.023


21.666


23.589


10


2.156


2.558


3.247


3.940


4.865


15.987


18.307


20.483


23.209


25.188







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






A.



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.






B.



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.


Your answer is correct.




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.






Compute the test statistic.

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


Find the ciritical value


Do we reject or fail to reject the hypothesis because there is sufficent or insufficent information?


Jun 09, 2022
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