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Chapter 15: Problem 28

Give an example of a situation where it would be appropriate to use a chi- square test of independence. Describe the population that would be sampled and the two variables that would be recorded.

Short Answer

Expert verified
Example: A car rental company wishes to know if the age group of a customer is independent of the preferred car model. The population to be sampled would be customers of the company and the two variables to be recorded would be 'Age Group' and 'Car Model'. These data points can be analyzed using a chi-square test of independence.

Step by step solution

01

Problem Situation

Consider a situation where a car rental company offers three car models - Compact, Sedan, and SUV. The company wants to know if customer preference for car model is independent of their age group (Young, Middle Aged, and Elderly). The two categorical variables are 'Car Model' and 'Age Group'.
02

Sampling and Data Collection

The company should undertake a survey that would help collect relevant data on customer preferences. The population to be sampled would be the company's customers. A random sample of customers would be selected and data on their age group and car model preference would be recorded.
03

Chi-Square Test of Independence

The chi-square test of independence would be used to analyze the collected data. Each response from the survey contributes to the count in one of the cells of a contingency table. The chi-square test is conducted to determine if the observed distribution of counts matches the distribution that would be expected if car model preference and age group were independent.

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Most popular questions from this chapter

The paper "Overweight Among Low-Income Preschool Children Associated with the Consumption of Sweet Drinks" (Pediatrics [2005]: 223-229) described a study of children who were underweight or normal weight at age 2 . Children in the sample were classified according to the number of sweet drinks consumed per day and whether or not the child was overweight one year after the study began. Is there evidence of an association between whether or not children are overweight after one year and the number of sweet drinks consumed? Assume that the sample of children in this study is representative of 2 - to 3 -year-old children, Test the appropriate hypotheses using a 0.05 significance level.

The following passage is from the paper "Gender Differences in Food Selections of Students at a Historically Black College and University" (College Student Journal \([2009]: 800-806):\) Also significant was the proportion of males and their water consumption ( 8 oz. servings) compared to females \(\left(X^{2}=8.166, P=.086\right) .\) Males came closest to meeting recommended daily water intake ( 64 oz. or more) than females \((29.8 \%\) vs. \(20.9 \%)\) This statement was based on carrying out a chi-square test of homogeneity using data in a two-way table where rows corresponded to gender (male, female) and columns corresponded to number of servings of water consumed per day, with categories none, one, two to three, four to five, and six or more. a. What hypotheses did the researchers test? What is the number of degrees of freedom associated with the reported value of the \(X^{2}\) statistic? b. The researchers based their statement on a test with a significance level of 0.10 . Would they have reached the same conclusion if a significance level of 0.05 had been used? Explain.

A particular cell phone case is available in a choice of four different colors. A store sells all four colors. To test the hypothesis that sales are equally divided among the four colors, a random sample of 100 purchases is identified. a. If the resulting \(X^{2}\) value were \(6.4,\) what conclusion would you reach when using a test with significance level \(0.05 ?\) b. What conclusion would be appropriate at significance level 0.01 if \(X^{2}=15.3 ?\) c. If there were six different colors rather than just four, what would you conclude if \(X^{2}=13.7\) and a test with \(\alpha=0.05\) was used?

Explain the difference between situations that would lead to a chi-square goodness-of-fit test and those that would lead to a chi-square test of homogeneity.

Does viewing angle affect a person's ability to tell the difference between a female nose and a male nose? This important (?) research question was examined in the article "You Can Tell by the Nose: Judging Sex from an Isolated Facial Feature" (Perception [1995]: \(969-973\) ). Eight Caucasian males and eight Caucasian females posed for nose photos. The article states that none of the volunteers wore nose studs or had prominent nasal hair. Each person placed a black Lycra tube over his or her head in such a way that only the nose protruded through a hole in the material. Photos were then taken from three different angles: front view, three-quarter view, and profile. These photos were shown to a sample of undergraduate students. Each student in the sample was shown one of the nose photos and asked whether it was a photo of a male or a female. The response was classified as either correct or incorrect. The accompanying table was constructed using summary values reported in the article. Is there evidence that the proportion of correct sex identifications differs for the three different nose views?
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