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AP Statistics with 6 Practice Tests

Martin Sternstein

Chapter 8

Inference for Categorical Data: Chi-Square - all with Video Answers

Educators

Section 29

Quiz 29

01:52

Problem 1

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 add - it with moon phase. The expected numbers are all $\frac{1}{4}(32+27+47+38)=36 .$ Which two categories contribute the largest components to the $\chi^{2}-$ test statistic?
(A) New moon and first quarter
(B) First quarter and full moon
(C) Full moon and last quarter
(D) New moon and full moon
(E) First quarter and last quarter

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
01:32

Problem 2

A random sample of 100 former student-athletes are picked from each of the colleges that 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. 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) A chi-square goodness-of-fit test for a uniform distribution
(B) A chi-square test of independence
(C) A chi-square test of homogeneity
(D) A multiple-sample $z$ -test of proportions
(E) A multiple-population $z$ -test of proportions

Jerrah Biggerstaff
Jerrah Biggerstaff
Numerade Educator
01:32

Problem 3

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 or she prefers hip-hop, pop, or alternative. A chi-square test of homogeneity of proportions is performed, and the resulting $P$ -value is below o. 05 . Which of the following is a proper conclusion?
(A) There is sufficient evidence that for all three music choices, the proportion of middle school students who prefer each choice is equal to the corresponding proportion of high school students.
(B) There is sufficient evidence that the proportion of middle school students who prefer hip-hop is different from the proportion of high school students who prefer hip-hop.
(C) There is sufficient evidence that for all three music choices, the proportion of middle school students who prefer each choice is different from the corresponding proportion of high school students.
(D) There is sufficient evidence that for at least one of the three music choices, the proportion of middle school students who prefer that choice is equal to the corresponding proportion of high school students.
(E) There is sufficient 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.

Jerrah Biggerstaff
Jerrah Biggerstaff
Numerade Educator
01:19

Problem 4

Given a two-way table, it's not obvious whether to perform a test for independence or a test for homogeneity. What is the main difference between the tests?
(A) How expected counts are calculated
(B) How $d f$, the degrees of freedom, is calculated
(C) The number of rows in the table
(D) The number of columns in the table
(E) The number of samples

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
02:01

Problem 5

Refer to the following. In a random sample of 525 teenagers, eye colors are cross-classified with favorite colors from among green, red, blue, and purple. Below is a two-way table of the responses.
For performing a chi-square test, which of the following is the appropriate null hypothesis?
(A) Favorite color choices among all teenagers are $20 \%$ green, $20 \%$ red, $20 \%$ blue, $20 \%$ purple, and $20 \%$ other.
(B) There is no difference between the distributions of color
choices among teenagers with different eye colors in this sample.
(C) There is no difference between the distributions of color choices among teenagers with different eye colors in the population of all teenagers.
(D) There is no association between eye color and favorite color among teenagers in this sample.
(E) There is no association between eye color and favorite color among teenagers in the population of all teenagers.

Meredith Kempson
Meredith Kempson
Numerade Educator
01:45

Problem 6

Refer to the following. In a random sample of 525 teenagers, eye colors are cross-classified with favorite colors from among green, red, blue, and purple. Below is a two-way table of the responses.
Which of the following is the expected count of blue-eyed teenagers who choose blue as their favorite color?
(A) 6
(B) 21
(C) 23.4
(D) 28.2
(E) 30

Meredith Kempson
Meredith Kempson
Numerade Educator
01:32

Problem 7

Refer to the following. In a random sample of 525 teenagers, eye colors are cross-classified with favorite colors from among green, red, blue, and purple. Below is a two-way table of the responses.
What is the degrees of freedom, $d f$, for the chi-square test on these data?
(A) 4
(B) 5
(C) 16
(D) 24
(E) 25

Meredith Kempson
Meredith Kempson
Numerade Educator
02:44

Problem 8

Refer to the following. In a random sample of 525 teenagers, eye colors are cross-classified with favorite colors from among green, red, blue, and purple. Below is a two-way table of the responses.
For these data, $\chi^{2}=18.591$ with a $P$ -value of 0.290 . Assuming a significance level of $0.05,$ which of the following is true?
(A) A Type-I error may have been committed, but a TypeII error was not committed.
(B) A Type-II error may have been committed, but a Type-I error was not committed.
(C) Both Type-I and Type-II errors may have been committed.
(D) Neither a Type-I nor a Type-II error could have been committed.
(E) There is not sufficient information to make any statements about the possibility of a Type-I or a Type-II error being committed.

Meredith Kempson
Meredith Kempson
Numerade Educator