Question 1

Which of the following statements is not correct?

Accepted Answer

A) The chi-squared test of independence is a one-sample test. 
B) Both variables in the chi-squared test of independence are nominal variables. 
C) The chi-squared goodness-of-fit test involves two categorical variables. 
D) The chi-squared distribution is skewed to the right. 
A) The chi-squared test of independence is a one-sample test. 
B) Both variables in the chi-squared test of independence are nominal variables. 
C) The chi-squared goodness-of-fit test involves two categorical variables. 
D) The chi-squared distribution is skewed to the right.

Question 2

A chi-squared goodness-of-fit test can be conducted either as a two-tail test or as a one-tail test.

Accepted Answer

A) True 
 B)False

Question 3

Like that of the Student t-distribution, the shape of the chi-squared distribution depends on its number of degrees of freedom.

Accepted Answer

A) True 
 B)False

Question 4

A left-tailed area in the chi-squared distribution equals 0.10. For 5 degrees of freedom, the table value equals 9.23635.

Accepted Answer

A) True 
 B)False

Question 5

A particular insurance company wants to investigate whether the gender and age of a client are related. A random sample of 350 clients of this insurance company was taken. $$\begin{array} { | l | c | c | c | } 
\hline  & { \text { Age group } } \
\hline  & 25 \text { and under } & \begin{array} { c } 
\text { Over } 25 \text { and } \
\text { under } 50
\end{array} & 50 \text { and over } \
\hline \text { Male } & 35 & 60 & 68 \
\hline \text { Female } & 65 & 80 & 42 \
\hline
\end{array}$$ Conduct a test to determine whether gender and age group are independent, using α of 0.01.

Accepted Answer

H_o: Gender and age group are independent

Question 6

Suppose that a random sample of 100 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardised and the number of observations in each of the intervals below was counted. Can we infer at the 10% significance level that the data were drawn from a normal population? $$\begin{array} { | c | c | } 
\hline \text { Intervals } & \text { Frequency } \
\hline Z \leq - 1 & 12 \
\hline - 1  1 & 20 \
\hline
\end{array}$$

Accepted Answer

@#IMG-DLM& , @#IMG-DLM& @#IMG-DLM& @#IMG-DLM& (the population is normal). H_A: At

Question 7

Which statistical technique is appropriate when we describe a single population of nominal data with two or more categories?

Accepted Answer

A) Z-test of the difference between two proportions. 
B) Chi-squared test of a multinomial experiment. 
C) Chi-squared test of a contingency table. 
D) Z test for one proportion. 
E) None of these choices are correct 
A) Z-test of the difference between two proportions. 
B) Chi-squared test of a multinomial experiment. 
C) Chi-squared test of a contingency table. 
D) Z test for one proportion. 
E) None of these choices are correct

Question 8

If we want to perform a one-tail test for differences between two populations of nominal data with exactly two categories, we must employ the z-test of $p _ { 1 } - p _ { 2 }$ .

Accepted Answer

A) True 
 B)False

Question 9

A right-tailed area in the chi-squared distribution equals 0.01. For 4 degrees of freedom, the table value equals 13.2767.

Accepted Answer

A) True 
 B)False

Question 10

A coffee machine sales representative visits 5 businesses per day. A sample of 200 days gives the frequencies of coffee machine sales volumes listed below: $$\begin{array} { | c | c | } 
\hline \text { Number of sales } & \text { Observed frequency (days) } \
\hline 0 & 10 \
\hline 1 & 38 \
\hline 2 & 69 \
\hline 3 & 63 \
\hline 4 & 18 \
\hline 5 & 2 \
\hline
\end{array}$$ Assume that the population is binomially distributed with a probability of purchase p = 0.50.
Should the assumption of a binomial distribution be rejected at the 1% significance level?

Accepted Answer

H₀: The population has a binomial probabi

Question 11

A sport preference poll showed the following data for men and women: $$\begin{array} { | l | c | c | c | c | c | } 
\hline & &&{ \text { Favourite Sport } } \
\hline \text { Gender } & \text { Rugby } & \text { B asketball } & \text { Football } & \text { Golf } & \text { Tennis } \
\hline \text { Male } & 24 & 17 & 30 & 18 & 22 \
\hline \text { Female } & 21 & 20 & 22 & 12 & 28 \
\hline
\end{array}$$ Using the 5% level of significance, test to determine whether sport preferences depend on gender.

Accepted Answer

H₀: The two variables (gender and favorit

Question 12

One type of Chi-squared goodness of fit test is a Chi-squared test for normality.

Accepted Answer

A) True 
 B)False

Question 13

Which of the following best describes the number of degrees of freedom used in a Chi-squared test of independence if there is a contingency table with 5 rows and 3 columns?

Accepted Answer

A) 7 
B) 8 
C) 15 
D) 10 
A) 7 
B) 8 
C) 15 
D) 10

Question 14

To determine whether a single coin is fair, the coin was tossed 200 times. The observed frequencies with which each of the two sides of the coin turned up are recorded as 112 heads and 88 tails. Is there sufficient evidence at the 5% significance level to allow you to conclude that the coin is not fair?

Accepted Answer

@#IMG-DLM& 0.50, @#IMG-DLM& = 0.50 (the coin is fair). H_A: At

Question 15

Which of the following tests do not use the Chi-squared distribution?

Accepted Answer

A) Test of a contingency table. 
B) Goodness-of-fit test. 
C) Test for the difference between two population means. 
D) All of these choices are correct. 
A) Test of a contingency table. 
B) Goodness-of-fit test. 
C) Test for the difference between two population means. 
D) All of these choices are correct.

Question 16

Consider a multinomial experiment involving n = 200 trials and k = 5 cells. The observed frequencies resulting from the experiment are shown in the following table: $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Cell } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Frequency } & 16 & 44 & 56 & 48 & 36 \
\hline
\end{array}$$ The null hypothesis to be tested is as follows.
H0 : p1 = 0.05, p2 = 0.25, p3 = 0.35, p4 = 0.20, p5 = 0.15.
Test the hypothesis at the 5% level of significance.

Accepted Answer

H0 : p₁ = 0.05, p₂ = 0.25, p₃ = 0.35, p₄ = 0

Question 17

Explain what is meant by the rule of five.

Accepted Answer

The rule of five requires that the expec

Question 18

The middle 0.95 portion of the chi-squared distribution with 9 degrees of freedom has table values of 3.32511 and 16.9190, respectively.

Accepted Answer

A) True 
 B)False

Question 19

The vice-chancellor of a university collected data from students concerning the building of a new library, and classified the responses into different categories (strongly agree, agree, undecided, disagree, strongly disagree) and according to whether the student was male or female. Which of the following tests should be used to test whether responses and gender are independent?

Accepted Answer

A) Chi-squared test for goodness-of-fit. 
B) Chi-squared test for normality. 
C) Chi-square test of a multinomial experiment. 
D) Chi-squared test of a contingency table. 
A) Chi-squared test for goodness-of-fit. 
B) Chi-squared test for normality. 
C) Chi-square test of a multinomial experiment. 
D) Chi-squared test of a contingency table.

Question 20

Which of the following is the correct decision in a goodness-of-fit test, if the calculated value of the test statistic is 20.08 and there are 10 categories, testing at 1% level of significance?

Accepted Answer

A) We reject Ho because p-value < 0.01. 
B) We do not reject Ho because p-value < 0.01. 
C) We reject Ho because 0.01 < p-value < 0.025. 
D) We do not reject Ho because 0.01 < p-value < 0.025. 
A) We reject Ho because p-value < 0.01. 
B) We do not reject Ho because p-value < 0.01. 
C) We reject Ho because 0.01 < p-value < 0.025. 
D) We do not reject Ho because 0.01 < p-value < 0.025.

Which of the following statements is not correct?

A chi-squared goodness-of-fit test can be conducted either as a two-tail test or as a one-tail test.

Like that of the Student t-distribution, the shape of the chi-squared distribution depends on its number of degrees of freedom.

A left-tailed area in the chi-squared distribution equals 0.10. For 5 degrees of freedom, the table value equals 9.23635.

Which statistical technique is appropriate when we describe a single population of nominal data with two or more categories?

If we want to perform a one-tail test for differences between two populations of nominal data with exactly two categories, we must employ the z-test of $p _ { 1 } - p _ { 2 }$ .

A right-tailed area in the chi-squared distribution equals 0.01. For 4 degrees of freedom, the table value equals 13.2767.

A sport preference poll showed the following data for men and women: Favourite Sport Gender Rugby B asketball Football Golf Tennis Male 24 17 30 18 22 Female 21 20 22 12 28 Using the 5% level of significance, test to determine whether sport preferences depend on gender.

One type of Chi-squared goodness of fit test is a Chi-squared test for normality.

Which of the following best describes the number of degrees of freedom used in a Chi-squared test of independence if there is a contingency table with 5 rows and 3 columns?

Which of the following tests do not use the Chi-squared distribution?

Explain what is meant by the rule of five.

The middle 0.95 portion of the chi-squared distribution with 9 degrees of freedom has table values of 3.32511 and 16.9190, respectively.

Which of the following is the correct decision in a goodness-of-fit test, if the calculated value of the test statistic is 20.08 and there are 10 categories, testing at 1% level of significance?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

Exam 14: Additional Tests for Nominal Data: Chi-Squared Tests

Which of the following statements is not correct?

A chi-squared goodness-of-fit test can be conducted either as a two-tail test or as a one-tail test.

Like that of the Student t-distribution, the shape of the chi-squared distribution depends on its number of degrees of freedom.

A left-tailed area in the chi-squared distribution equals 0.10. For 5 degrees of freedom, the table value equals 9.23635.

Which statistical technique is appropriate when we describe a single population of nominal data with two or more categories?

If we want to perform a one-tail test for differences between two populations of nominal data with exactly two categories, we must employ the z-test of p1−p2p _ { 1 } - p _ { 2 }p1​−p2​ .

A right-tailed area in the chi-squared distribution equals 0.01. For 4 degrees of freedom, the table value equals 13.2767.

A sport preference poll showed the following data for men and women: Favourite Sport Gender Rugby B asketball Football Golf Tennis Male 24 17 30 18 22 Female 21 20 22 12 28 Using the 5% level of significance, test to determine whether sport preferences depend on gender.

One type of Chi-squared goodness of fit test is a Chi-squared test for normality.

Which of the following best describes the number of degrees of freedom used in a Chi-squared test of independence if there is a contingency table with 5 rows and 3 columns?

Which of the following tests do not use the Chi-squared distribution?

Explain what is meant by the rule of five.

The middle 0.95 portion of the chi-squared distribution with 9 degrees of freedom has table values of 3.32511 and 16.9190, respectively.

Which of the following is the correct decision in a goodness-of-fit test, if the calculated value of the test statistic is 20.08 and there are 10 categories, testing at 1% level of significance?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

If we want to perform a one-tail test for differences between two populations of nominal data with exactly two categories, we must employ the z-test of $p _ { 1 } - p _ { 2 }$ .