Asked by William McGinnis on May 29, 2024
Verified
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 from 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. Classification \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Classification } Classification
Book reader Non-book reader Non- reader Total Less than $15,00017326755495$15,000 to $24,99916813019317$25,000 to $39,9991601449313$40,000 and over 213883304 Total 714629861429\begin{array}{|l|c|c|c|c|}\hline&\begin{array}{c}\text { Book } \\\text { reader }\end{array} & \begin{array}{c}\text { Non-book } \\\text { reader }\end{array} & \begin{array}{c}\text { Non- } \\\text { reader }\end{array} & \text { Total }\\\hline\begin{array}{l}\text { Less than } \\\$ 15,000\end{array} & 173 & 267 & 55 & 495 \\\hline\begin{array}{l}\$ 15,000 \text { to } \\\$ 24,999\end{array} & 168 & 130 & 19 & 317 \\\hline\begin{array}{l}\$ 25,000 \text { to } \\\$ 39,999\end{array} & 160 & 144 & 9 & 313 \\\hline \begin{array}{l}\$ 40,000 \text { and } \\\text { over }\end{array} & 213 & 88 & 3 & 304 \\\hline \text { Total } & 714 & 629 & 86 & 1429 \\\hline\end{array} Less than $15,000$15,000 to $24,999$25,000 to $39,999$40,000 and over Total Book reader 173168160213714 Non-book reader 26713014488629 Non- reader 55199386 Total 4953173133041429
Household
Income
A) H0: There is no relationship between household income and book readership. HA: Household income and book readership are not related.
B) H0: The classifications do not have the same distribution for each household income bracket. HA: The classifications have the same distribution for each household income bracket.
C) H0: Household income and book readership are independent. HA: Household income and book readership are not dependent.
D) H0: The classifications have the same distribution for each household income bracket. HA: The classifications do not have the same distribution for each household income bracket.
E) H0: There is a relationship between household income and book readership. HA: Household income and book readership are not related.
Book Readership
The number or demographic profile of people who read books.
Household Income
The total amount of money earned by every member of a single household.
- Employ chi-square tests for the evaluation of hypotheses related to the distribution of categorical data.
- Analyze the outcomes of chi-square assessments for independence and goodness-of-fit.
Verified Answer
KA
Katrina AzucenaMay 29, 2024
Final Answer :
D
Explanation :
The null hypothesis (H0) states that the classifications have the same distribution for each household income bracket. This means that the proportions of book readers, non-book readers, and non-readers are the same across different income brackets. The alternative hypothesis (HA) states that the classifications do not have the same distribution for each household income bracket, which implies that the proportions of book readers, non-book readers, and non-readers vary across different income brackets. This is the appropriate hypothesis test for determining whether or not there is a relationship between household income and book readership. Hence, the correct choice is D.
Learning Objectives
- Employ chi-square tests for the evaluation of hypotheses related to the distribution of categorical data.
- Analyze the outcomes of chi-square assessments for independence and goodness-of-fit.
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