Deck 16: Inference for Counts: Chi-Square Tests

Question 1

Consider the following to answer the question(s) below:
An online book store wants to determine if there is an association between coupon redemption and gender. After a special coupon broadcast to its reward members, the following data on coupon redemption at checkout were collected.
At α = 0.05

A) We reject the null hypothesis.
B) We fail to reject the null hypothesis.
C) We can conclude that there is an association between coupon redemption and gender.
D) We reject the null hypothesis and can conclude that there is an association between coupon redemption and gender.
E) We fail to reject the null hypothesis and can conclude that there is an association between coupon redemption and gender.

Answer 1

D

Question 2

Consider the following to answer the question(s) below:
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.

How many degrees of freedom are appropriate to test that arrivals are uniformly distributed?

A) 4
B) 100
C) 5
D) 6
E) 99

Answer 2

A

Question 3

Consider the following to answer the question(s) below:
An online book store wants to determine if there is an association between coupon redemption and gender. After a special coupon broadcast to its reward members, the following data on coupon redemption at checkout were collected.
What Chi-Square test is appropriate in this situation?

A) Goodness of Fit
B) Homogeneity
C) Independence
D) Proportional
E) No Chi-Square test is appropriate in this situation.

Answer 3

C

Question 4

Consider the following to answer the question(s) below:
An online book store wants to determine if there is an association between coupon redemption and gender. After a special coupon broadcast to its reward members, the following data on coupon redemption at checkout were collected.
The degrees of freedom associated with the test statistic are

A) 1
B) 2
C) 3
D) 4
E) 330

Question 5

Consider the following to answer the question(s) below:
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.

What is the value of the test statistic?

A) 2.50
B) 7.7794
C) 3.62
D) 2.46
E) 6.94

Question 6

By examining residuals, determine which type of property had the most impact on the test results? What are the implications for the real estate agency?

Question 7

A real estate agency, located in a metropolitan area in Canada., kept data on the various types of properties purchased in the area. Historically, 15% of purchases were for condominiums, 30% were for townhouses, 40% for single family homes, 10% for commercial properties, and 5% for land. With changing demographics, the agency wondered if the current distribution matches the historical distribution. Recent data showed the following:
a. State appropriate hypotheses to test whether the purchasing agent is correct.
b. What is the value of the test statistic and its associated P-value?
c. State the conclusion at α = 0.05.

Question 8

Consider the following to answer the question(s) below:
Vending machines on a college campus offer a variety of drinks. The purchasing agent believes that each type of drink is equally preferred by students and consequently orders equal quantities. The number of drinks sold from vending machines on this campus for the last six months is shown in the following table.

What is the value of the mode in this case?

A) 1
B) 2
C) 3
D) 4
E) Cannot be determined with the information available.

Question 9

Consider the following to answer the question(s) below:
A local cell phone provider wants to determine if the use of text messaging is independent of age. The following data has been collected from a random sample of customers.

Based on the data above what is the expected frequency for the "under 21 and regularly use text messaging" cell?

A) 56.8
B) 120
C) 145
D) 62
E) 50

Question 10

By examining residuals, determine which type of drink had the most impact on the test results? What are the implications for the purchasing agent?

Question 11

Consider the following to answer the question(s) below:
Vending machines on a college campus offer a variety of drinks. The purchasing agent believes that each type of drink is equally preferred by students and consequently orders equal quantities. The number of drinks sold from vending machines on this campus for the last six months is shown in the following table.

What is the mean of the χ2 distribution in this case?

A) 3
B) 4
C) 2
D) 1
E) Cannot be determined with the information available.

Question 12

Consider the following to answer the question(s) below:
Vending machines on a college campus offer a variety of drinks. The purchasing agent believes that each type of drink is equally preferred by students and consequently orders equal quantities. The number of drinks sold from vending machines on this campus for the last six months is shown in the following table.

The correct value of the test statistic is

A) χ2 = 8.012
B) χ2 = 12.019
C) χ2 = 0.984
D) χ2 = 45.014
E) χ2 = 64.192

Question 13

A manufacturing plant for recreational vehicles receives shipments from three different parts vendors. There has been a defect issue with some of the electrical wiring in the recreational vehicles manufactured at the plant. The plant manager believes that the defect issue is dependent on the parts vendor. The plant manager reviews a sample of quality assurance inspections from the last six months.
a. State appropriate hypotheses to test the plant manager's belief.
b. What is the value of the test statistic and its associated P-value?
c. State the conclusion at α = 0.05.

Question 14

Consider the following to answer the question(s) below:
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.

At α = 0.05

A) We fail to reject the null hypothesis and can conclude that arrivals are uniformly distributed based on this sample.
B) We reject the null hypothesis.
C) We reject the null hypothesis and can conclude that arrivals are not uniformly distributed based on this sample.
D) We fail to reject the null hypothesis.
E) We conclude that arrivals are uniformly distributed.

Question 15

Consider the following to answer the question(s) below:
An online book store wants to determine if there is an association between coupon redemption and gender. After a special coupon broadcast to its reward members, the following data on coupon redemption at checkout were collected.
The correct value of the test statistic is

A) χ2 = 5.339
B) χ2 = 8.429
C) χ2 = 0.839
D) χ2 = 45.556
E) χ2 = 28.505

Question 16

Consider the following to answer the question(s) below:
Vending machines on a college campus offer a variety of drinks. The purchasing agent believes that each type of drink is equally preferred by students and consequently orders equal quantities. The number of drinks sold from vending machines on this campus for the last six months is shown in the following table.

The degrees of freedom associated with the test statistic are

A) 1
B) 2
C) 3
D) 4
E) 679

Question 17

Consider the following to answer the question(s) below:
Vending machines on a college campus offer a variety of drinks. The purchasing agent believes that each type of drink is equally preferred by students and consequently orders equal quantities. The number of drinks sold from vending machines on this campus for the last six months is shown in the following table.

At α = 0.05

A) We reject the null hypothesis.
B) We fail to reject the null hypothesis.
C) We conclude that the purchasing agent was not correct.
D) We reject the null hypothesis and conclude that the purchasing agent was not correct.
E) We fail to reject the null hypothesis and conclude that the purchasing agent was not correct.

Question 18

An online book store wants to determine if coupon redemption is independent of gender. After a special coupon broadcast to its reward members, the following data on coupon redemption at checkout were collected. a. State appropriate hypotheses to determine whether coupon redemption is independent of gender.
b. What is the value of the test statistic and its associated P-value?
c. State the conclusion at α = .05.

Question 19

Consider the following to answer the question(s) below:
Vending machines on a college campus offer a variety of drinks. The purchasing agent believes that each type of drink is equally preferred by students and consequently orders equal quantities. The number of drinks sold from vending machines on this campus for the last six months is shown in the following table.

The correct null hypothesis to test if the purchasing agent is correct can be worded as

A) The types of drinks are not equally (uniformly) distributed among the students buying drinks.
B) The types of drinks are equally (uniformly) distributed among the students buying drinks.
C) The types of drinks are independent from each other.
D) The distribution of type of drink purchases follows the normal distribution.
E) The distribution of type of drink purchases follows a Poisson distribution.

Question 20

Vending machines on a college campus offer a variety of drinks. The purchasing agent believes that each type of drink is equally preferred by students and consequently orders equal quantities. The number of drinks sold from vending machines on this campus for the last six months is shown in the following table.
a. State appropriate hypotheses to test whether the purchasing agent is correct.
b. What is the value of the test statistic and its associated P-value?
c. State the conclusion at α = 0.05.

Question 21

Consider the following to answer the question(s) below:
A local cell phone provider wants to determine if the use of text messaging is independent of age. The following data has been collected from a random sample of customers.

The value of the test statistic is

A) 92.2095
B) 0
C) 9.2104
D) 11.0705
E) 275.02

Question 22

Consider the following to answer the question(s) below:
A local cell phone provider wants to determine if the use of text messaging is independent of age. The following data has been collected from a random sample of customers.

To conduct the independence test the correct degrees of freedom are

A) 2
B) 3
C) 6
D) 5
E) 4

Question 23

Consider the following to answer the question(s) below:
We want to test whether type of car owned (domestic or foreign) is independent of gender. The following are the results of a random sample of 990 car owners.

The value of the test statistic is

A) 3.34
B) 3.54
C) 3.84
D) 33.44
E) 8.54

Question 24

Consider the following to answer the question(s) below:
We want to test whether type of car owned (domestic or foreign) is independent of gender. The following are the results of a random sample of 990 car owners.

To conduct the independence test the correct degrees of freedom are

A) 1
B) 4
C) 2
D) 3
E) 5

Question 25

Consider the following to answer the question(s) below:
We want to test whether type of car owned (domestic or foreign) is independent of gender. The following are the results of a random sample of 990 car owners.

At α = 0.05

A) We fail to reject the null hypothesis and can conclude that there is no association between gender and the type of car owned (domestic or foreign).
B) We reject the null hypothesis and can conclude that there is an association between gender and the type of car owned (domestic or foreign).
C) We reject the null hypothesis.
D) We fail to reject the null hypothesis.
E) We can conclude that gender and the type of car owned (domestic or foreign) are unrelated.

Question 26

Consider the following to answer the question(s) below:
A local cell phone provider wants to determine if the use of text messaging is independent of age. The following data has been collected from a random sample of customers.

At α = 0.05

A) We reject the null hypothesis and can conclude that there is an association between age and the use of text messaging.
B) We fail to reject the null hypothesis.
C) We fail to reject the null hypothesis and can conclude that there is no association between age and the use of text messaging.
D) We reject the null hypothesis.
E) We can conclude that age and use of text messaging are related.