Deck 10: Testing Hypotheses About Proportions

Question 1

A report on the U.S. economy indicates that 28% of Americans have experienced difficulty in making mortgage payments. A news organization randomly sampled 400 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) 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 For testing this claim are

A)
B)
C)
D)
E)

Answer 1

Question 2

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 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) None of the above.

Answer 2

The data do not provide convincing evidence that the marketing campaign increases
The percentage of customers for the company's products.

Question 3

A company manufacturing computer chips finds that 8% of all chips manufactured are defective. 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. A hypothesis Test is performed to determine if the additional training was 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 ..

Answer 3

z = -1.56

Question 4

Suppose minorities form 29% of a local population. A local business has 125 employees, of which 28 are minorities. Did the business discriminate in its hiring
Practices?

A) There is sufficient evidence that the business discriminated in its hiring practices.
B) We cannot draw any direct conclusions from these data.
C) The company should institute examine its recruitment and hiring practices based on
These data.
D) There is no evidence that the business discriminated in its hiring practices.
E) Both A and C

Question 5

A survey claims that 7 out of 10 customers recommend Western Drugs for pharmacy issues. To test this claim, a random sample of 100 customers is obtained from the list of Rewards customers. Of these 100 customers, 75 indicate that they recommend using Western Drugs for pharmacy needs. We would like to know if this claim is accurate.

A)
B)
C)
D)
E)

Question 6

A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has Encouraged their professional employees to engage in local service activities. They Believe that at least 40% or more of the employees engage in these types of activities. If This is not the case, they will institute an incentive program to increase community Involvement. The correct null and alternative hypotheses to test the belief of top Management are

A)
B)
C)
D)
E)

Question 7

A national study report released by the Center for Studying Health System Change (HSC) in 2010, indicated that 20.9% of Americans were identified as having medical bill
Financial issues. Many people in families with problems paying medical bills in 2010
Experienced severe financial consequences from their medical debt, with about two-thirds
Reporting problems paying for other necessities and a quarter considering bankruptcy, the
Study found. What if a news organization randomly sampled 400 Americans from 10
Cities and found that 90 reported having such difficulty. A test was done to investigate
Whether the problem is more severe among these cities. The p-value for this test is

A) 0.2156
B) 0.0539
C) 0.1078
D) 0.4312
E) None of the above.

Question 8

A company manufacturing computer chips finds that 8% of all chips manufactured are defective. 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. A hypothesis
Test is performed to determine if the additional training was 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) None of the above.

Question 9

A report on the U.S. economy indicates that 28% of Americans have experienced
difficulty in making mortgage payments. A news organization randomly sampled 400
Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine,
August 2008) and found that 136 reported such difficulty. Does this indicate that the
problem is more severe among these cities?
A. Write the null and alternative hypotheses.
b. What is the value of the test statistic?
c. What is the associated P-value?
d. State your conclusion using α = 0.05.

Question 10

A business school has found that over the years, out of all the students who are offered
admission, the proportion who accept is 0.70. After a new director of admissions is
hired, the university wants to check if the proportion of students accepting has changed
significantly. Suppose they offer admission to 1200 students and 888 accept. Is this
evidence of a change from the status quo?
A. Write the null and alternative hypotheses.
b. Let's perform a one sample z-test for proportions: What is the value of the test statistic?
c. What is the associated P-value?
d. State your conclusion using α = 0.05.

Question 11

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 in a test market so that the effectiveness of the marketing
campaign may be evaluated.
A. Write the null and alternative hypotheses.
b. 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 12

Suppose minorities form 29% of a local population. A local business has 125
employees, of which 28 are minorities. Did the business discriminate in its hiring
practices?
A. Write the null and alternative hypotheses.
b. What is the value of the test statistic?
c. What is the associated P-value?
d. State your conclusion using α = 0.05.

Question 13

A survey claims that 7 out of 10 customers recommend Western Drugs for pharmacy
issues. To test this claim, a random sample of 100 customers is obtained from the list of
rewards customers. Of these 100 customers, 75 indicate that they recommend using
Western Drugs for pharmacy needs. We would like to know if this claim is accurate.
Use alpha = 0.05
A. Write the null and alternative hypotheses.
b. Let's perform a one sample z-test for proportions: What is the value of the test statistic?
c. What is the associated P-value?

Question 14

A company that has a 10% market share launches a marketing campaign. At the end
of the campaign period, the company conducts a survey in order to assess whether its
market share has increased. The result of the survey issued to 500 customers was 12.5%.
A. Write the null and alternative hypotheses.
b. What is the value of the test statistic?
c. What is the associated P-value?
d. State your conclusion using α = 0.05.

Question 15

If a P-value = 0.1039 at α = 0.05

A) The result is inconclusive, we need to know the proportions compared.
B) We reject the null hypothesis.
C) We cannot conclude anything unless we know the sample size.
D) We fail to reject the null hypothesis.
E) The value of α is too large to be meaningful.

Question 16

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?
A. Write the null and alternative hypotheses.
b. What is the value of the test statistic?
c. What is the associated P-value?
d. State your conclusion using α = 0.01.

Question 17

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 is the P-value for this proportion test?

A) 0.0297
B) 0.0594
C) 0.1638
D) 0.1188
E) 0.5940

Question 18

Suppose that you are conducting a two tailed test about a proportion at the 0.01 level of significance. The correct critical value(s) to be used in drawing a conclusion is (are)

A) ± 1.96
B) ±2.575
C) -1.645
D) ±1.645
E) 1.96

Question 19

Business decisions should always take into consideration which of the following?

A) The statistical significance of the test.
B) The cost of the proposed action.
C) The effect size.
D) Both A and B, not C.
E) A. B, and C.

Question 20

A report on the U.S. economy indicates that 28% of Americans have experienced difficulty in making mortgage payments. A news organization randomly sampled 400 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) 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 for Testing this claim is

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

Question 21

A national study report released by the Center for Studying Health System Change (HSC) in 2010, indicated that 20.9% of Americans were identified as having medical bill
Financial issues. Many people in families with problems paying medical bills in 2010
Experienced severe financial consequences from their medical debt, with about two-thirds
Reporting problems paying for other necessities and a quarter considering bankruptcy, the
Study found. What if a news organization randomly sampled 400 Americans from 10
Cities and found that 90 reported having such difficulty. A test was done to investigate
Whether the problem is more severe among these cities. The result of this test is

A) Inconclusive.
B) There is no indication the medical bill problem is more severe among the cities
Surveyed.
C) There is insufficient evidence to conduct the test.
D) There is evidence that the medical bill problem is more severe among the cities
Surveyed.
E) None of the above.

Question 22

A national study report released by the Center for Studying Health System Change (HSC) in 2010, indicated that 20.9% of Americans were identified as having medical bill
Financial issues. Many people in families with problems paying medical bills in 2010
Experienced severe financial consequences from their medical debt, with about two-thirds
Reporting problems paying for other necessities and a quarter considering bankruptcy, the
Study found. What if a news organization randomly sampled 400 Americans from 10
Cities and found that 90 reported having such difficulty. A test was done to investigate
Whether the problem is more severe among these cities. What is the value of the test
Statistic?

A) 0.787
B) 0.016
C) -0.787
D) 2.479
E) None of the above.

Question 23

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. Consequently the company conducts a program for employees in order to Reinforce the new corporate philosophy. After the program is completed, employees are Surveyed to see if a greater percentage is now open to innovativeness and change. The Correct alternative hypothesis is

A)
B)
C)
D)
E)

Question 24

A satellite TV provider finds that 15% of their customers switch providers when a discount offer expires. A consultant tries a small experiment and offers a random sample
Of customers a free 6 months of service if they commit to staying as a customer for two
Years. Not surprisingly, they find that the new switching rate is lower by a statistically
Significant amount. Should they offer short-term discounts to all their customers?

A) The p-value of the hypothesis test.
B) The cost of the service.
C) How much the switch is lowered (the effect size).
D) A, B and C.
E) Both B and C.

Question 25

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. Consequently the company conducts a program for employees in order to Reinforce the new corporate philosophy. Based on data collected after the program, the Finds the 95% confidence interval for the proportion of all employees open to new ideas To be 18% to 22%. What should the company conclude?

A) The null hypothesis should not be rejected.
B) There is no evidence to suggest that the program improved employees' attitudes Toward innovativeness and change.
C) There is evidence that the program improved employees' attitudes toward Innovativeness and change.
D) Both A and B.
E) Both A and C.

Question 26

A survey claims that 7 out of 10 customers recommend Western Drugs for pharmacy issues. To test this claim, a random sample of 100 customers is obtained from the list of
Rewards customers. Of these 100 customers, 75 indicate that they recommend using
Western Drugs for pharmacy needs. We would like to know if this claim is accurate.
State your conclusion using α = 0.05.

A) The null hypothesis is not supported: more than 70% of customers recommend
Western Drugs for pharmacy issues.
B) The null hypothesis is not supported: less than 70% of customers recommend Western
Drugs for pharmacy issues.
C) The null hypothesis is not supported: the percentage of customers who recommend
Western Drugs for pharmacy issues is not equal to 75%.
D) More information is required to draw a valid conclusion
E) The null hypothesis is supported: 70% of customers recommend Western Drugs for
Pharmacy issues.

Question 27

A company that has a 10% market share launches a marketing campaign. At the end of the campaign period, the company conducts a survey in order to assess whether its
Market share has increased. The result of the survey issued to 500 customers was 12.5%.
What is the associated p-value?

A) 0.0314
B) 0.1256
C) 0.0628
D) 0.0066
E) None of the above