Deck 15: Inference for Counts: Chi-Square Tests

Question 1

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 1

We are 95% confident that there is no difference between the proportions of patients reporting drowsiness for the two allergy medications.

Question 2

An online department 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.

Answer 2

Independence

Question 3

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%

Answer 3

-4% to 9%

Question 4

Vending machines on a college campus offer a variety of snacks.The purchasing agent believes that each type of snack 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 snacks are not uniformly distributed among the students buying snacks
B)the types of snacks are uniformly distributed among the students buying snacks
C)the types of snacks are independent from each other
D)the distribution of type of snack purchases follows the normal distribution
E)None of the above.

Question 5

Vending machines on a college campus offer a variety of snacks.The purchasing agent believes that each type of snack is equally preferred by students and consequently orders equal quantities.The number of snacks 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 candy bars would we expect to have been sold?

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

Question 6

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

Question 7

Vending machines on a college campus offer a variety of snacks.The purchasing agent believes that each type of snack is equally preferred by students and consequently orders equal quantities.The number of snacks sold from vending machines on this campus for the last six months is shown in the following table.The appropriate test to see if the purchasing agent is correct is the ________________________ .

A)chi-square test of independence
B)z-test for two proportions
C)chi-square goodness-of-fit test
D)chi-square test of homogeneity
E)normality test

Question 8

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 9

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 ________________________ .

A)χ ² = 8.10
B)χ ² = 6.52
C)χ ² = 5.03
D)χ ² = 7.40
E)χ ² = 9.89

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.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 11

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 12

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:

The value of the Chi-square test statistic is

A)χ ² = 5.993
B)χ ² = 62.538
C)χ ² = 101.482
D)χ ² = 77.431
E)χ ² = 8.101

Question 13

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.

Question 14

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

Question 15

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

Question 16

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 17

Vending machines on a college campus offer a variety of snacks.The purchasing agent believes that each type of snack is equally preferred by students and consequently orders equal quantities.The number of snacks 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 ________________________ .

A)χ ² = 8.012
B)χ ² = 12.019
C)χ ² = 0.984
D)χ ² = 45.014
E)None of the above.