# Interpret the results of the chi-square test. The Book Industry Study Group, Inc., performs...

## Question:

Interpret the results of the chi-square test. The Book Industry Study Group, Inc., 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. ?2 = 114.534; P-value = 2.287  10-22 Select one: a. There is not sufficient evidence to reject the null hypothesis and conclude that income and classification are independent. b. There is sufficient evidence to reject the null hypothesis and conclude that income and classification are dependent. c. There is sufficient evidence to reject the null hypothesis and conclude that the classifications are not uniformly distributed for each income bracket. d. There is not sufficient evidence to reject the null hypothesis and conclude that income and classification are dependent. e. There is sufficient evidence to reject the null hypothesis and conclude that income and classification are independent. Interpret the results of the chi-square test. The Book Industry Study Group, Inc., 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 stx 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 stx months prior to the survey. The following data were obtained from a random sample of 1429 persons 16 years old and over. Classification Book Non-book Non Total 495 317 313 304 readerreader reader Less than $15,000 173 267 Household$15,000 to168 130 Income $24,999 19$25,000 to $39,999$40,000 and213 88 over 160 144 Total714629 86 1429 x2-114.534; P-value 2.287 x 1022 Select one: a. There is not sufficient evidence to reject the null hypothesis and conclude that income and classification are independent. b. There is sufficient evidence to reject the null hypothesis and conclude that income and classification are dependent. ?c. There is sufficient evidence to reject the null hypothesis and conclude that the classifications are not uniformly distributed for each income bracket. O dThere is not sufficient evidence to reject the null hypothesis and conclude that income and classification are dependent. e. There is sufficient evidence to reject the null hypothesis and conclude that income and classification are independent.

## Test for independence

Chi-square test is used to test homogeneity, independence and to check the underlying distribution. The test for independence it is required to check whether the change in categories induces any significant change in the other category involved.

## Answer and Explanation: 1

a

Given Information

Book readers are classified as:

1. A book reader is defined to be one who read one or more books in the six months prior to the survey;

2. 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;

3. A nonreader is defined to be one who did not read a book, newspaper, or magazine in the six months prior to the survey.

Sample size of survey is 1429

The P-value is {eq}2.287 \times {10^{ - 22}} {/eq}

The hypothesis states that,

{eq}{H_o}: {/eq} The income and classification of book readers is independent

{eq}{H_a}: {/eq}The income and classification are not independent.

Since the P-value is very small, as compared to assumed significance value of 0.01, the null hypothesis must be rejected and hence it can be concluded that the income and classification are not independent.

In other words there is sufficient evidence to reject the null hypothesis and conclude that income and classification are dependent.

Therefore Option B is true.

#### Learn more about this topic:

The Chi-Square Test

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Chapter 2 / Lesson 13
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What if you expect one thing, but get another? The chi-square test is a method of statistical analysis that can help us identify if the results from a genetic cross are simply due to chance, or if something else is happening. Learn about the chi-square test in this lesson.