Deck 12: Testing Hypotheses About Proportions

Question 1

Consider the following to answer the question(s) below:
A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand. A marketing director suggests that the company invest in new advertising and labeling to strengthen its green image. The company decides to do so but in a test market so that the effectiveness of the marketing campaign may be evaluated.
Based on data collected in the test market, the company constructed a 98% confidence interval for the proportion of all consumers who might buy their brand. The resulting interval is 16% to 28%. What conclusion should the company reach about the new marketing campaign? Explain.

Answer 1

The confidence interval contains the hypothesized value of 19.5%. Therefore the data do not provide convincing evidence that the marketing campaign increases the percentage of customers for the company's products.

Question 2

Consider the following to answer the question(s) below:
A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that high employee turnover is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. Was the additional training effective in lowering the defect rate?
Write the null and alternative hypotheses.

Answer 2

H0 : p = 0.08 and HA : p < 0.08

Question 3

Consider the following to answer the question(s) below:
Top management of a large multinational corporation wants to create a culture of innovativeness and change. A consultant hired to assess the company's organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work. One of his recommendations is for the company to conduct seminars for employees in order to disseminate and reinforce the new corporate philosophy. This is done for a six month trial period after which its value in changing employee attitudes will be assessed.
In this context, describe the Type II error possible. How might such an error impact the company?

Answer 3

A Type II error would be failing to detect an increase in the percentage of employees open to new ideas, when in fact it has. The company would miss an opportunity to increase the percentage of employees with more innovative attitudes.

Question 4

Consider the following to answer the question(s) below:
A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that high employee turnover is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. Was the additional training effective in lowering the defect rate?
Which of the following statement is true about this hypothesis test?

A) It is a two-tailed test about a proportion.
B) It is a one-tailed test about a mean.
C) It is a one-tailed test about a proportion.
D) It is a two-tailed test about a mean.
E) No hypothesis test can be conducted with the given information.

Question 5

Consider the following to answer the question(s) below:
Suppose that a report indicates that 28% of Canadians have experienced difficulty in making mortgage payments. Further suppose that a news organization randomly sampled 400 Canadians from 10 cities and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities?
What is the value of the test statistic?

Question 6

Consider the following to answer the question(s) below:
Top management of a large multinational corporation wants to create a culture of innovativeness and change. A consultant hired to assess the company's organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work. One of his recommendations is for the company to conduct seminars for employees in order to disseminate and reinforce the new corporate philosophy. This is done for a six month trial period after which its value in changing employee attitudes will be assessed.
Based on data collected after the trial period, the company constructed a 95% confidence interval for the proportion of all employees open to new ideas and approaches toward their work. The resulting interval is 18% to 22%. What conclusion should the company reach about the seminars? Explain.

Question 7

Consider the following to answer the question(s) below:
A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that high employee turnover is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. Was the additional training effective in lowering the defect rate?
The correct value of the test statistic is

A) z = -1.56
B) z = 2.57
C) z = 1.56
D) z = 1.96
E) z = -2.57

Question 8

Consider the following to answer the question(s) below:
Suppose that a report indicates that 28% of Canadians have experienced difficulty in making mortgage payments. Further suppose that a news organization randomly sampled 400 Canadians from 10 cities and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities?
State your conclusion using α = 0.05.

Question 9

Consider the following to answer the question(s) below:
Suppose that a report indicates that 28% of Canadians have experienced difficulty in making mortgage payments. Further suppose that a news organization randomly sampled 400 Canadians from 10 cities and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities?
What is the associated P-value?

Question 10

Consider the following to answer the question(s) below:
Suppose that a report indicates that 28% of Canadians have experienced difficulty in making mortgage payments. Further suppose that a news organization randomly sampled 400 Canadians from 10 cities and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities?
Write the null and alternative hypotheses.

Question 11

Consider the following to answer the question(s) below:
A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand. A marketing director suggests that the company invest in new advertising and labeling to strengthen its green image. The company decides to do so but in a test market so that the effectiveness of the marketing campaign may be evaluated.
In this context, describe the Type II error possible. How might such an error impact the company?

Question 12

Consider the following to answer the question(s) below:
A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that high employee turnover is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. Was the additional training effective in lowering the defect rate?
The P-value associated with the test statistic is

A) 0.01
B) 0.05
C) 0.2339
D) 0.0594
E) 0.0075

Question 13

Consider the following to answer the question(s) below:
A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand. A marketing director suggests that the company invest in new advertising and labeling to strengthen its green image. The company decides to do so but in a test market so that the effectiveness of the marketing campaign may be evaluated.
In this context, describe the Type I error possible. How might such an error impact the company?

Question 14

Consider the following to answer the question(s) below:
A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand. A marketing director suggests that the company invest in new advertising and labeling to strengthen its green image. The company decides to do so but in a test market so that the effectiveness of the marketing campaign may be evaluated.
Write the null and alternative hypotheses.

Question 15

Consider the following to answer the question(s) below:
A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that high employee turnover is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. Was the additional training effective in lowering the defect rate?
What is the associated P-value?

Question 16

Consider the following to answer the question(s) below:
A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that high employee turnover is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. Was the additional training effective in lowering the defect rate?
State your conclusion using α = 0.01.

Question 17

Consider the following to answer the question(s) below:
A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that high employee turnover is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. Was the additional training effective in lowering the defect rate?
What is the value of the test statistic?

Question 18

Consider the following to answer the question(s) below:
Top management of a large multinational corporation wants to create a culture of innovativeness and change. A consultant hired to assess the company's organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work. One of his recommendations is for the company to conduct seminars for employees in order to disseminate and reinforce the new corporate philosophy. This is done for a six month trial period after which its value in changing employee attitudes will be assessed.
Write the null and alternative hypotheses.

Question 19

Consider the following to answer the question(s) below:
A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that high employee turnover is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. Was the additional training effective in lowering the defect rate?
At α = 0.01

A) We can conclude that the additional training significantly lowered the defect rate.
B) We can conclude that the additional training did not significantly lower the defect rate.
C) We can conclude that the additional training significantly increased the defect rate.
D) We can conclude that the additional training did not affect the defect rate.
E) No conclusion can be made with the given information.

Question 20

Consider the following to answer the question(s) below:
Top management of a large multinational corporation wants to create a culture of innovativeness and change. A consultant hired to assess the company's organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work. One of his recommendations is for the company to conduct seminars for employees in order to disseminate and reinforce the new corporate philosophy. This is done for a six month trial period after which its value in changing employee attitudes will be assessed.
In this context, describe the Type I error possible. How might such an error impact the company?

Question 21

Consider the following to answer the question(s) below:
Winnipeg Pet Plus believes that it has a market share of 25 percent of the local dog food market. It surveys 100 dog owners and ask whether or not it is their regular source of dog food, and 23 people say yes.
At α = 0.05

A) We cannot conclude that the percentage of customers who buy their dog food regularly at Winnipeg Pet Plus is significantly different from 25%.
B) We can conclude that the percentage of customers who buy their dog food regularly at Winnipeg Pet Plus is equal to 25%.
C) We can conclude that the percentage of customers who buy their dog food regularly at Winnipeg Pet Plus is significantly lower than 25%.
D) We cannot conclude that the percentage of customers who buy their dog food regularly at Winnipeg Pet Plus is significantly lower than 25%.
E) We can conclude that the percentage of customers who buy their dog food regularly at Winnipeg Pet Plus is not significantly lower than 25%.

Question 22

Consider the following to answer the question(s) below:
Winnipeg Pet Plus believes that it has a market share of 25 percent of the local dog food market. It surveys 100 dog owners and ask whether or not it is their regular source of dog food, and 23 people say yes.
The correct value of the test statistic is

A) -0.462
B) -0.475
C) 0.462
D) 0.475
E) -0.456

Question 23

Consider the following to answer the question(s) below:
Suppose that a report indicates that 28% of Canadians have experienced difficulty in making mortgage payments. Further suppose that a news organization randomly sampled 400 Canadians from 10 cities and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities?
At α = 0.05

A) We can conclude that the percentage of Canadians in these cities experiencing difficulty making mortgage payments is significantly higher than 28%.
B) We can conclude that the percentage of Canadians in these cities experiencing difficulty making mortgage payments is significantly lower than 28%.
C) We can conclude that the percentage of Canadians in these cities experiencing difficulty making mortgage payments is not significantly different from 28%.
D) We can conclude that the percentage of Canadians in these cities experiencing difficulty making mortgage payments is equal to 28%.
E) No conclusion can be drawn with the given information.

Question 24

Consider the following to answer the question(s) below:
After completing sales training for a large company, it is expected that a salesperson will generate a sale on at least 15 percent of the calls he or she makes. To make sure that the sales training process is working, a random sample of 400 sales calls made by sales representatives who have completed the training have been selected and the null hypothesis is to be tested at 0.05 alpha level. Suppose that a sale is made on 76 of the calls.
The appropriate null and alternative hypotheses are

A) H0 : p = 0.15 and HA : p > 0.15
B) H0 : p >0.15 and HA : p = 0.15
C) H0 : p = 0.15 and HA : p< 0.15
D) H0 : p < 0.15 and HA : p = 0.15
E) H0 : p = 0.15 and HA : p ≠ 0.15

Question 25

Consider the following to answer the question(s) below:
Winnipeg Pet Plus believes that it has a market share of 25 percent of the local dog food market. It surveys 100 dog owners and ask whether or not it is their regular source of dog food, and 23 people say yes.
In this context, committing a Type I error

A) occurs when they conclude that the percentage of customers using Winnipeg Pet Plus for their dog food is not 25% when in fact it is
B) occurs when they conclude that the percentage of customers using Winnipeg Pet Plus for their dog food is less than 25% when in fact it has not
C) occurs when they conclude that the percentage of customers using Winnipeg Pet Plus for their dog food is 25% when in fact it has not
D) occurs when they conclude that the percentage of customers using Winnipeg Pet Plus for their dog food is 25% when in fact it is less than that
E) occurs when they conclude that the percentage of customers using Winnipeg Pet Plus for their dog food is more than 25% when in fact it is less than that

Question 26

Consider the following to answer the question(s) below:
Winnipeg Pet Plus believes that it has a market share of 25 percent of the local dog food market. It surveys 100 dog owners and ask whether or not it is their regular source of dog food, and 23 people say yes.
The appropriate null and alternative hypotheses are

A) H0 : p = 0.25 and HA : p ≠ 0.25
B) H0 : p = 0.25 and HA : p > 0.25
C) H0 : p > 0.25 and HA : p = 0.25
D) H0 : p ≠ 0.25 and HA : p = 0.25
E) H0 : p = 0.25 and HA : p < 0.25

Question 27

Consider the following to answer the question(s) below:
Suppose that a report indicates that 28% of Canadians have experienced difficulty in making mortgage payments. Further suppose that a news organization randomly sampled 400 Canadians from 10 cities and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities?
The correct null and alternative hypotheses are

A) H0 : p = 0.28 and HA : p > 0.28
B) H0 : p = 0.28 and HA : p < 0.28
C) H0 : p = 0.28 and HA : p ≠ 0.28
D) H0 : p ≠ 0.28 and HA : p = 0.28
E) H0 : p > 0.28 and HA : p = 0.28

Question 28

Consider the following to answer the question(s) below:
A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand. A marketing director suggests that the company invest in new advertising and labeling to strengthen its green image. The company decides to do so but in a test market so that the effectiveness of the marketing campaign may be evaluated.
In this context, committing a Type I error

A) occurs when they conclude that the percentage of customers purchasing the company's brand has decreased when in fact it has not
B) occurs when they conclude that the percentage of customers purchasing the company's brand has not increased when in fact it has
C) would result in the company spending money on a new marketing campaign that does increase the percentage of customers buying their brand
D) occurs when they conclude that the percentage of customers purchasing the company's brand has increased when in fact it has not and would result in the company wasting money on a new marketing campaign that does not increase the percentage of customers buying their brand
E) would have absolutely no effect on the company

Question 29

Consider the following to answer the question(s) below:
After completing sales training for a large company, it is expected that a salesperson will generate a sale on at least 15 percent of the calls he or she makes. To make sure that the sales training process is working, a random sample of 400 sales calls made by sales representatives who have completed the training have been selected and the null hypothesis is to be tested at 0.05 alpha level. Suppose that a sale is made on 76 of the calls.
The correct value of the test statistic is

A) 2.24
B) 1.96
C) -2.24
D) 3.34
E) -1.645

Question 30

Consider the following to answer the question(s) below:
Winnipeg Pet Plus believes that it has a market share of 25 percent of the local dog food market. It surveys 100 dog owners and ask whether or not it is their regular source of dog food, and 23 people say yes.
The P-value associated with the test statistic is

A) 0.644
B) 0.322
C) 0.678
D) 0.635
E) 0.317

Question 31

Consider the following to answer the question(s) below:
An advertising agency has developed a new ad for one of the national car manufacturing companies. The agency is interested in testing whether the proportion of favourable responses to the ad is the same between male versus female adults. It plans on conducting the test using an alpha level equal to 0.05. A sample of 100 adults of each gender will be used in the study. Each person will be asked to view the ad and indicate whether they find the ad to be "pleasing" or not. The samples resulted in 57 males and 47 females that liked the ad.
The correct value of the test statistic is

A) 1.42
B) 1.645
C) 2.234
D) 1.024
E) -2.234

Question 32

Consider the following to answer the question(s) below:
Suppose that a report indicates that 28% of Canadians have experienced difficulty in making mortgage payments. Further suppose that a news organization randomly sampled 400 Canadians from 10 cities and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities?
The P-value associated with the test statistic is

A) 0.025
B) 0.2119
C) 136.0177
D) 0.0522
E) 0.0038

Question 33

Consider the following to answer the question(s) below:
After completing sales training for a large company, it is expected that a salesperson will generate a sale on at least 15 percent of the calls he or she makes. To make sure that the sales training process is working, a random sample of 400 sales calls made by sales representatives who have completed the training have been selected and the null hypothesis is to be tested at 0.05 alpha level. Suppose that a sale is made on 76 of the calls.
At α = 0.05

A) We can conclude that the percentage of sales after training is significantly higher than 15%.
B) We can conclude that the percentage of sales after training is significantly lower than 15%.
C) We can conclude that the percentage of sales after training is equal to 15%.
D) We can conclude that the percentage of sales after training is no different than 15%.
E) We can conclude that the percentage of sales after training is not significantly higher than 15%.

Question 34

Consider the following to answer the question(s) below:
An advertising agency has developed a new ad for one of the national car manufacturing companies. The agency is interested in testing whether the proportion of favourable responses to the ad is the same between male versus female adults. It plans on conducting the test using an alpha level equal to 0.05. A sample of 100 adults of each gender will be used in the study. Each person will be asked to view the ad and indicate whether they find the ad to be "pleasing" or not. The samples resulted in 57 males and 47 females that liked the ad.
The appropriate null and alternate hypotheses are

A) H0 : p1 = p2 and HA : p1 ≠ p2
B) H0 : p1 = p2 and HA : p1 > p2
C) H0 : p1 > p2 and HA : p1 ≠ p2
D) H0 : p1 ≠ p2 and HA : p1 = p2
E) H0 : p1 = p2 and HA : p1 < p2

Question 35

Consider the following to answer the question(s) below:
Suppose that a report indicates that 28% of Canadians have experienced difficulty in making mortgage payments. Further suppose that a news organization randomly sampled 400 Canadians from 10 cities and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities?
The correct value of the test statistic is

A) z = 1.28
B) z = -2.67
C) z = 2.67
D) z = 1.96
E) z = -1.28

Question 36

Consider the following to answer the question(s) below:
A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand. A marketing director suggests that the company invest in new advertising and labeling to strengthen its green image. The company decides to do so but in a test market so that the effectiveness of the marketing campaign may be evaluated.
Based on data collected in the test market, the company constructed a 98% confidence interval for the proportion of all consumers who might buy their brand. The resulting interval is 16% to 28%. What conclusion should the company reach about the new marketing campaign?

A) The data do not provide convincing evidence that the marketing campaign increases the percentage of customers for the company's products.
B) The data do provide convincing evidence that the marketing campaign increases the percentage of customers for the company's products.
C) The new marketing campaign is effective in increasing the percentage of customers buying their brand.
D) The company should launch the new marketing campaign.
E) No conclusion can be reached based on the given information.