A publishing company performs sample surveys to obtain information on characteristics of book readers.A book reader is defined to be one who read one or more books in the six months prior to the survey;a non-book reader is defined to be one who read newspapers or magazines but no books in the six months prior to the survey;a nonreader is defined to be one who did not read a book,newspaper,or magazine in the six months prior to the survey.The following data were obtained in a random sample of 1429 persons 16 years old and over in an effort to determine whether or not the proportions of book readers,non-book readers,and non-readers are the same for each income bracket.Use a 1% level of significance.

= 114.534;P-value = 2.287 ×
A)There is not sufficient evidence to reject the null hypothesis and conclude that the distributions of reader classification and household income are different.
B)There is sufficient evidence to reject the null hypothesis and conclude that the distributions of reader classification and household income are the same.
C)There is sufficient evidence to reject the null hypothesis and conclude that the distributions of reader classification and household income are different.
D)There is sufficient evidence to reject the null hypothesis and conclude that the reader classification is dependent on household income.
E)There is not sufficient evidence to reject the null hypothesis and conclude that the distributions of reader classification and household income are the same.

Question

A publishing company performs sample surveys to obtain information on characteristics of book readers.A book reader is defined to be one who read one or more books in the six months prior to the survey;a non-book reader is defined to be one who read newspapers or magazines but no books in the six months prior to the survey;a nonreader is defined to be one who did not read a book,newspaper,or magazine in the six months prior to the survey.The following data were obtained in a random sample of 1429 persons 16 years old and over in an effort to determine whether or not the proportions of book readers,non-book readers,and non-readers are the same for each income bracket.Use a 1% level of significance.

= 114.534;P-value = 2.287 ×

= 114.534;P-value = 2.287 × 
A)There is not sufficient evidence to reject the null hypothesis and conclude that the distributions of reader classification and household income are different. 
B)There is sufficient evidence to reject the null hypothesis and conclude that the distributions of reader classification and household income are the same. 
C)There is sufficient evidence to reject the null hypothesis and conclude that the distributions of reader classification and household income are different. 
D)There is sufficient evidence to reject the null hypothesis and conclude that the reader classification is dependent on household income. 
E)There is not sufficient evidence to reject the null hypothesis and conclude that the distributions of reader classification and household income are the same.

Quizplus · Accepted Answer

The null hypothesis is that the proportions of book readers, non-book readers, and non-readers are the same for each income bracket. The alternative hypothesis is that they are different. 
To test this hypothesis, a chi-square test for independence can be used. Using a significance level of 0.01 and 2 degrees of freedom, the critical value of chi-square is 11.345. 
The calculated chi-square value is 114.534 with a corresponding P-value of 2.287 x 10^-24. Since the calculated chi-square value exceeds the critical value and the P-value is less than the significance level, there is sufficient evidence to reject the null hypothesis and conclude that the distributions of reader classification and household income are different. Therefore, the best choice is C.

A Publishing Company Performs Sample Surveys to Obtain Information on Characteristics