Deck 12: Testing Hypotheses About Proportions

Question 1

What is the associated P-value?

Answer 1

P-value = 0.0594

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

State your conclusion using α = 0.01.

Answer 3

At α = 0.01 we fail to reject the null hypothesis. At the 0.01 level of significance, we cannot conclude that the additional training significantly lowered the defect rate.

Question 4

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 5

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 6

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 7

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 for the company is 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 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?
What is the value of the test statistic?

Question 9

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 for the company is 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?

Question 10

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.

Question 11

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 12

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 13

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 statements 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) It is a two-tailed test about a standard deviation.

Question 14

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 significantly affected the defect rate.
E) we can conclude that the additional training probably increased the defect rate..

Question 15

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 for the company is 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 16

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 17

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 18

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 19

What is the value of the test statistic?

Question 20

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 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. They survey 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 22

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 23

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. They survey 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 significantly different from 25% when in fact it is not.
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 24

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 and female adults. It conducted the test using an alpha level of 0.05. A sample of 100 adults of each gender was used in the study. Each person was asked to view the ad and indicate whether they found the ad to be "pleasing" or not. The samples resulted in 57 males and 47 females that liked the ad.
The appropriate null and alternative 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 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. They survey 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 26

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 and female adults. It conducted the test using an alpha level of 0.05. A sample of 100 adults of each gender was used in the study. Each person was asked to view the ad and indicate whether they found 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 27

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 more than 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 28

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 more than 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 29

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) we can conclude that the percentage of Canadians in these cities experiencing difficulty making mortgage payments is less than or equal to 28% .

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. They survey 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 precisely equal to 25.00%.
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 can conclude that the percentage of customers who buy their dog food regularly at Winnipeg Pet Plus is significantly higher than 25%.
E) there is strong evidence that the percentage of customers who buy their dog food regularly at Winnipeg Pet Plus is significantly different from 25%.

Question 31

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 32

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. They survey 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 33

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 proportion of customers purchasing the company's products.
B) The data do provide convincing evidence that the marketing campaign increases by 2% the proportion of customers purchasing the company's products.
C) The data do provide convincing evidence that the marketing campaign increases by 12% the proportion of customers purchasing the company's products.
D) The data do provide convincing evidence that the marketing campaign decreases by 2% the proportion of customers purchasing the company's products.
E) The data do provide convincing evidence that the marketing campaign decreases by 12% the proportion of customers purchasing the company's products.

Question 34

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 more than 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 not significantly different from 15%.
E) We can conclude that the percentage of sales after training is not significantly higher than 15%.

Question 35

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 36

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.