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Chapter 11: Problem 23

Describe in your own words a test of independence and a test of homogeneity. Give one example of each.

Short Answer

Expert verified
A test of independence determines if two categorical variables are independent using a contingency table and chi-square test. An example is analyzing the relationship between gender and choosing a college major. A test of homogeneity checks if different groups have the same distribution of a categorical variable and also uses a chi-square test. An example is determining if males and females have similar preferences for movie genres.

Step by step solution

01

Defining Test of Independence

A test of independence is a statistical test used to determine whether two categorical variables are independent of each other or not. It's performed using a contingency table and applying a chi-square test.
02

Example of Test of Independence

An example of a test of independence could be analyzing whether there's a relationship between gender (male, female) and choosing a major in college (Science, Liberal Arts).
03

Defining Test of Homogeneity

A test of homogeneity is a statistical way to determine whether different populations (groups) have the same distribution of a categorical variable. It involves comparing observed and expected frequencies of categories with chi-square testing.
04

Example of Test of Homogeneity

As for an example of a test of homogeneity; consider an experiment to determine if males and females have same preferences for movie genres (Horror, Comedy, Action, Romance).

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Most popular questions from this chapter

A forestry official is comparing the causes of forest fires in two regions, \(\mathrm{A}\) and \(\mathrm{B}\). The following table shows the causes of fire for 76 randomly selected recent fires in these two regions. $$ \begin{array}{lcccc} \hline & \text { Arson } & \text { Accident } & \text { Lightning } & \text { Unknown } \\ \hline \text { Region A } & 6 & 9 & 6 & 10 \\ \text { Region B } & 7 & 14 & 15 & 9 \\ \hline \end{array} $$

Find the value of \(\chi^{2}\) for 4 degrees of freedom and A. \(.005\) area in the right tail of the chi-square distribution curve b. \(.05\) area in the left tail of the chi-square distribution curve

Each of five boxes contains a large (but unknown) number of red and green marbles. You have been asked to find if the proportions of red and green marbles are the same for each of the five boxes. You sample 50 times, with replacement, from each of the five boxes and observe \(20,14,23,30\), and 18 red marbles, respectively. Can you conclude that the five boxes have the same proportions of red and green marbles? Use a \(.05\) level of significance.

National Electronics Company buys parts from two subsidiaries. The quality control department at this company wanted to check if the distribution of good and defective parts is the same for the supplies of parts received from both subsidiaries. The quality control inspector selected a sample of 300 parts received from Subsidiary A and a sample of 400 parts received from Subsidiary \(\mathrm{B}\). These parts were checked for being good or defective. The following table records the results of this investigation. $$ \begin{array}{lcc} \hline & \text { Subsidiary A } & \text { Subsidiary B } \\ \hline \text { Good } & 284 & 381 \\ \text { Defective } & 16 & 19 \\ \hline \end{array} $$ Using a \(5 \%\) significance level, test the null hypothesis that the distributions of good and defective parts are the same for both subsidiaries.

Home Mail Corporation sells products by mail. The company's management wants to find out if the number of orders received at the company's office on each of the 5 days of the week is the same. The company took a sample of 400 orders received during a 4 -week period. The following table lists the frequency distribution for these orders by the day of the week. $$ \begin{array}{l|ccccc} \hline \text { Day of the week } & \text { Mon } & \text { Tue } & \text { Wed } & \text { Thu } & \text { Fri } \\ \hline \text { Number of orders received } & 92 & 71 & 65 & 83 & 89 \\ \hline \end{array} $$ Test at a \(5 \%\) significance level whether the null hypothesis that the orders are evenly distributed over all days of the week is true.
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