Deck 15: Inference for Counts: Chi-Square

Question 1

Find expected counts.
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. The expected number of perfect
Parts from Made-4-U Co. is

A) 75.9
B) 91.08
C) 71
D) 61.81
E) 252

Answer 1

A

Question 2

Create and interpret a confidence interval for the difference of two proportions.
Before being released to market, a drug company tests a new allergy medication for
Potential side effects. A random sample of 160 individuals with allergies was selected for
The study. The new allergy medication was randomly assigned to 80 of them, and another
Popular allergy medication already on the market (Brand C) was assigned to the rest. Out
Of the 80 given the new allergy medication, 14 reported drowsiness; 22 of the 80 taking
Brand C reported drowsiness. The 95% confidence interval for the difference in
Proportions reporting drowsiness is -0.028 to 0.228. Which of the following is correct?

A) We are 95% confident that there is no difference between the proportions of patients reporting drowsiness for the two allergy medications.
B) We are 95% confident that there is a difference between the proportions of patients reporting drowsiness for the two allergy medications.
C) We are 95% confident that the proportion of patients reporting drowsiness is higher for the new allergy medication.
D) We are 95% confident that the proportion of patients reporting drowsiness is lower for the new allergy medication.
E) There will be a significant difference between the proportions 95% of the time.

Answer 2

A

Question 3

Analyze a conclusion using standardized residuals.
A real estate agency, located in a metropolitan area in the northeastern U.S., 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:
What is the standardized residual associated with Townhouses?

A) 23.5
B) 4.85
C) 10.86
D) 2.38
E) Not enough information given to calculate.

Answer 3

D

Question 4

Apply the Chi-Square goodness-of-fit test.
A real estate agency, located in a metropolitan area in the northeastern U.S., 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:

Question 5

Find expected counts.
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. The expected number of rejected
Parts from Perfect Parts Co. is

A) 53
B) 51.51
C) 57.68
D) 61.81
E) 171

Question 6

Interpret confidence and prediction intervals.
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 check out were collected.

Question 7

Find expected counts.
A real estate agency, located in a metropolitan area in the northeastern U.S., 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:
Based on the historical distribution, we would expect how many homes to be purchased?

A) 121
B) 122.54
C) 130
D) 129.95
E) 100

Question 8

Choose the appropriate test.
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. Which Chi-square test is most
Appropriate for this situation?

A) Goodness of Fit
B) Homogeneity
C) Dependence
D) Proportional
E) None of the above.

Question 9

Apply the Chi-Square test of homogeneity.
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. The correct value of the test
Statistic for determining if the plant manager's belief is supported is

Question 10

Create and interpret a confidence interval for the difference of two proportions.
Previous surveys reported that more men than women trade stocks online. A local
Brokerage firm randomly selected a sample of investors. They found that 45 out of 234
Men traded online and 42 out of 251 women traded online. The 95% confidence interval
For the difference in proportions is

A) 4% to 9%
B) -4% to 9%
C) 2% to 12%
D) -2% to 12%
E) -2% to -4%

Question 11

Interpret confidence and prediction intervals.
A real estate agency, located in a metropolitan area in the northeastern U.S., 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 = .05.

Question 12

Apply the Chi-Square goodness-of-fit test.
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 for determining if the purchasing agent's belief if supported is

Question 13

Choose the appropriate test.
A real estate agency, located in a metropolitan area in the northeastern U.S., 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:
Which Chi-square test is most appropriate for this situation?

A) Goodness of Fit
B) Homogeneity
C) Independence
D) Proportional
E) None of the above.

Question 14

Interpret confidence and prediction intervals.
Determine which type of drink had the most impact on the test results. What are the
implications for the purchasing agent?

Question 15

Find expected counts.
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. If the purchasing agent is
Correct, how many Kiwi Strawberry drinks would we expect to have been sold?

A) 170
B) 198
C) 125
D) 180
E) 680

Question 16

Choose the appropriate test.
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 check out were collected. Which Chi-square test
Is most appropriate for this situation?

A) Goodness of Fit
B) Homogeneity
C) Independence
D) Proportional
E) None of the above.

Question 17

Apply the Chi-Square test of independence to test for an association.
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 check out were collected. The correct value of
The test statistic is

A) 2 = 5.339 χ
B) 2 χ = 8.429
C) 2 χ = 0.839
D) 2 = 45.556 χ
E) None of the above.

Question 18

Interpret confidence and prediction intervals.
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 = .05.

Question 19

State hypotheses.
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 null hypothesis to test his belief can be worded as

A) The types of drinks are not uniformly distributed among the students buying drinks.
B) The types of drinks are 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) None of the above.

Question 20

Analyze a conclusion using standardized residuals.
A real estate agency, located in a metropolitan area in the northeastern U.S., 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. Based on the data shown below, the null
Hypothesis was rejected and the agency concluded that the current distribution of property
Sales differs from the historical distribution. Based on an examination of the standardized
Residuals, which type of property had the most impact on the test results?

A) Condos
B) Townhouses
C) Homes
D) Commercial
E) Land