Ch. 15 Chi-Squared Test

Question 1

a random sample of mice is obtained, and each mouse is timed as it moves through a maze to a reward treat at the end. After several days of training, each mouse is timed again. The data should be analyzed using…
- a z-test of proportions
- s two-sample test of means
- a paired t-test
- a chi-square test
- a regression analysis

Answer 1

a paired t-test

Question 2

To test the claim that dogs bite more or less depending upon the phase of the moon, a university hospital counts admissions for dog bites and classifies with moon phase.
new moon: 32
first quarter: 27
full moon: 47
last quater: 38

which of the following is the proper conclusion?
- the data prove that the dog bites occur equally during all moon phases
- the data prove that dog bites do not occur equally during all moon phases
- the data give evidence that dog bites occur equally during all moo phases
- the data give evidence that dog bites do not occur equally during all moon phases
- the data do not give sufficient evidence to conclude that dog bites are related to moon phases.

Answer 2

the data do not give sufficient evidence to conclude that dog bites are related to moon phases

Question 3

For a project, a student randomly picks 100 fellow AP Statistics students to survey on whether each has either a PC or Apple at home (all students in the school have a home computer) and what score (1, 2, 3, 4, 5) each expects to receive on the AP exam. A chi-square test of independence results in a test statistic of 8. How many degrees of freedom are there?

Answer 3

four (4)

Question 4

A random sample of 100 former student-athletes are picked from each of the 16 colleges which are members of the Big East conference. Students are surveyed about whether or not they feel they received a quality education while participating in varsity athletics. A 2x16 table of counts is generated. Which of the following is the most appropriate test to determine whether there is a difference among these schools as to the student-athlete perception of having received a quality education.
- a chi-square godness-of-fit test fir a uniform distribution
- a chi-square test of independence
- a chi-square test of homogeneity of proportions
- a multiple-sample z-test of proportions
- a multiple-population z-test of proportions

Answer 4

a chi squared test of homogeneity of proportions

Question 5

According to theory, blood types in the general population occur in the following proportions: 46% O, 40% A, 10% B, and 4% AB. Anthropologists come upon a previously unknown civilization living on a remote island, A random sampling of blood types yields the following counts: 77 O, 85 A, 23 B, and 15 AB. Is there sufficient evidence to conclude that the distribution of blood types found among the island population differs from that which occurs in the general population?
- the data prove that blood type distribution on the island is different from that of the general population
- the data prove that blood type distribution on the island is not different from that of the general population
- the data give evidence at the 1% significance level that blood type distribution on the island is different from that of the general population
- the data give evidence at the 5% significance level, but not at the 1% significance level, that blood type distribution on the island is different from that of the general population
- the data do not give evidence at the 5% significance level that blood type distribution on the island is different from that of the general population

Answer 5

the data give evidence at the 5% significance level, but not at the 1% significance level, that blood type distribution on the island is different from that of the general population

Question 6

Is there a relationship between education level and sports interest? A study cross-classified 1,500 randomly selected adults in three categories of education level (not a high school graduate, high school graduate, and college graduate) and five categories of major sports interest (baseball, basketball. football. hockey, and tennis). The chi-squared value is 13.95. Is there evidence of a relationship between education level and sports interest?
- the data prove there is relationship between education level and sports interest
- the evidence points to a cause-and-effect relationship between education and sports interest
- there is evidence at the 5% significance level of a relationship between education level and sports interest
- there is evidence at the 10% significance level, but not at the 5% significance level, of a relationship between education level and sports interest
- the p-value is greater than .10, so there is no evidence of a relationship between education level and sports interest

Answer 6

there is evidence at the 10% significance level, but not at the 5% significance level, of a relationship between education level and sports interest

Question 7

A disc jockey wants to determine whether middle school students and high school students have similar music tastes. Independent random samples are taken from each group, and each person is asked whether he/she prefers hip-hop, pop, or alternative. A chi-square test pf homogeneity of proportions is performed, and the resulting p-value is below .05. Which of the following is a proper conclusion?

Answer 7

there is evidence that for at least one of the three music choices the proportion of middle school students who prefer that choice is different from the corresponding proportion of high school students

Question 8

a geneticist claims that four species of fruit flies should appear in the ratio 1:3:3:9. Suppose that a sample of 2000 flies contained 110,345, 360, and 1185 flies of each species, respectively. Is there sufficient evidence to reject the geneticist’s claim?

Answer 8

the data give sufficient evidence to reject the geneticist’s claim

Question 9

univariate categorical data

Answer 9

data that has one variable but many categories (k)

Question 10

bivariate categorical data

Answer 10

data from two categorical variables from one sample

Question 11

chi square

Answer 11

test statistic that measures how observed frequences and expected frequencies differ among categorical variables

Question 12

chi squared sampling distribution curve

Answer 12

• not symmetric (appears skewed)
• longer tail to the right
• no area associated with negative values
• many different distributions due to the different degrees of freedom