Deck 16: Inference for Counts: Chi-Square Tests

Question 1

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.

Answer 1

3.

Question 2

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.

Given α = 0.05. Using the χ2 table from the Appendix B, we get the critical value of

A) 7.815.
B) 9.488.
C) 11.070.
D) 9.348.
E) 12.838.

Answer 2

7.815.

Question 3

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?

Answer 3

Condominiums type of property has the highest standardized residual (5.765) and its χ2 component is the largest (33.232). More people bought condominiums than would have been expected based on the historical distribution. The real estate agency should try and list as many condominiums as possible.

Question 4

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 5

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 = 5.340.
B) χ2 = 8.429.
C) χ2 = 0.839.
D) χ2 = 45.556.
E) χ2 = 28.505.

Question 6

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) Normal distribution
E) Gosset's t

Question 7

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 preferred by the students buying drinks.
B) all types of drinks are equally preferred by the students.
C) the types of drinks are independent from each other.
D) the type of drink is dependent on gender of a student.
E) the type of drink is dependent on student's program.

Question 8

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 9

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 10

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 11

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 is

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

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.

What is not true about the expected frequencies?

A) Assuming that the null hypothesis is true, the expected frequencies are equal across the four types of drinks.
B) The value of an expected frequency needs not be an integer. However, in this case they all are equal to 170.
C) We use the total number of observations (680) to calculate the expected frequencies.
D) The expected frequencies are 0.234 (Lemon Lime), 0.291 (Kiwi Strawberry), 0.256 (Tropical Punch), and 0.219 (Grape).
E) The expected frequencies are all equal to (0.25) (680) = 170.

Question 13

Consider the following to answer the question(s) below:
A walk-in medical clinic believes that arrivals are equally 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 14

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 alternative hypothesis.
B) we fail to reject the null hypothesis.
C) we cannot conclude that there is an association between coupon redemption and gender.
D) we reject the null hypothesis and conclude that online coupon redemption and gender are not independent.
E) we know that online coupon redemption and gender are independent.

Question 15

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 alternative hypothesis.
B) we fail to reject the null hypothesis.
C) we conclude that the purchasing agent was correct.
D) we reject the null hypothesis and conclude that the purchasing agent was not correct. The drink options are not equally preferred by the students.
E) as the P-value is low (less than α), we conclude that all types of drinks are equally preferred by students.

Question 16

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 17

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 18

Consider the following to answer the question(s) below:
A walk-in medical clinic believes that arrivals are equally 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 conclude that arrivals are equally distributed based on this sample.
B) we reject the null hypothesis.
C) we fail to reject the alternative hypothesis and can conclude that arrivals are not equally distributed based on this sample.
D) we support the alternative hypothesis. There is strong evidence that arrivals are not the same over weekdays.
E) as the P-value = 0.645 is high, we conclude that arrivals are not equally distributed. Monday arrivals are the highest.

Question 19

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 20

Consider the following to answer the question(s) below:
A walk-in medical clinic believes that arrivals are equally 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 equally distributed?

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

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:
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. There is no evidence that use of text messaging is independent of age. We 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 alternative hypothesis and can conclude that use of text messaging is independent of age.
D) as the P-value < .0001 is very low, We reject the null hypothesis.there is no association between age and the use of text messaging.
E) since χ2 = 92.2095 > χcr2 = 5.991, we support the null hypothesis and can conclude that age and use of text messaging are not related.

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. There is no evidence that type of car owned (domestic or foreign) is dependent on gender.
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) as P-value = 0.0676 is fairly high, we support the alternative hypothesis.
D) we fail to reject the null alternative hypothesis. There is strong evidence that the type of car owned (domestic or foreign) is dependent on gender.
E) since χ2 = 3.34 < χcr2 = 3.841, 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:
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.