Chapter 17 The Chi-Square Statistic: Tests for Goodness of Fit and Independence

Problems

1. Explain how the chi-square tests differ from parametric tests (such as t tests or ANOVA)

with respect to the hypotheses, the data, and the assumptions underlying the test.

2. A researcher is interested consumer preferences among three brands of yogurt. A sample of

90 people is obtained, and each individual is asked to taste each brand and then select his/her

favorite. The resulting frequency data are as follows:

Brand A Brand B Brand C

37

21

32

Do the data indicate any significant preferences among the three brands? Test at the .05 level of

significance.

3. A researcher is interested in the relationship between IQ and longevity. A sample of n = 200

obituaries is selected from the newspaper and old school records are consulted to determine the

individuals' IQ scores when they were between the ages of 10 and 20. The individuals were

then classified into two IQ groups and three age groups at the time of death. The data are as

follows. Based on these results, is there a significant relationship between IQ and longevity?

Test with = .05.

Age at the time of death

< 60 60 to 75 > 75

IQ < 110

41

63

36

IQ 110

9

27

24

4. An insurance investigator has observed the people with some astrological signs tend to be

safer drivers the people with other signs. Using insurance records, the investigator classified 200

people according to their astrological signs and whether or not they were involved in a car

accident during the previous 12 months. The data are as follows:

Libra Leo Gemini

Accident

7

4

19

No Accident

73

46

51

Do the data indicate a significant relationship between sign and accidents? Test at the .05 level

of significance.

5. A researcher would like to know whether there is a consistent, predictable relationship

between verbal skills and math skills for high school students. A sample of 200 students is

obtained and each student is given a standardized English test and a standardized math test.

Based on the test results, students are classified as high or low for verbal skills and for math

skills. The results are summarized in the following frequency distribution:

Verbal Skills

High Low

High Math

59

41

Low Math

31

69

a. Based on these results, can the researcher conclude that there is a significant relationship

between verbal skills and math skills? Test at the .05 level of significance.

b. Compute the phi-coefficient to measure the strength of the relationship.