Deck 13: Testing Hypotheses

Question 1

Write the hypotheses.
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

Answer 1

A

Question 2

Identify the type of test.
Insurance companies track life expectancy information to assist in determining the cost
Of life insurance policies. Last year the average life expectancy of all policyholders was
77 years. ABI Insurance wants to determine if their clients now have a longer life
Expectancy, on average, so they randomly sample some of their recently paid policies.
The insurance company will only change their premium structure if there is evidence that
People who buy their policies are living longer than before. 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.

Answer 2

B

Question 3

Make conclusions based on confidence intervals.
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 3

A

Question 4

Make conclusions about the hypotheses.
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. Suppose the P-value associated with the test statistic is 0.0594. At α = .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 affect the defect rate.
E) None of the above.

Question 5

Write the hypotheses.
Insurance companies track life expectancy information to assist in determining the
Cost of life insurance policies. Last year the average life expectancy of all policyholders
Was 77 years. ABI Insurance wants to determine if their clients now have a longer life
Expectancy, on average, so they randomly sample some of their recently paid policies.
The insurance company will only change their premium structure if there is evidence that
People who buy their policies are living longer than before. The correct null and
Alternative hypotheses are

Question 6

Calculate the appropriate test statistic.
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

Question 7

Write the hypotheses.
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

Question 8

Make conclusions about the hypotheses.
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 the
Firm's professionals volunteer an average of more than 15 hours per month. If this is not
The case, they will institute an incentive program to increase community involvement. A
Random sample of 24 professionals yields a mean of 16.6 hours and a standard deviation
Of 2.22 hours. The P-value associated with the resulting test statistic is 0.0009. At α = 0.05, which of the following is the correct conclusion?

A) We reject the null hypothesis.
B) We fail to reject the null hypothesis.
C) The firm shouldn't need to institute an incentive program because the evidence indicates that professional employees volunteer an average of more than 15 hours per
Month in their local community.
D) Both A and C
E) Both B and C

Question 9

Identify the type of test.
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 10

Identify and interpret types of error.
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.
Suppose that based on the sample results the company rejects the null hypothesis when in
Fact it is true. Which of the following statements is correct?

A) This is known as a Type II error.
B) This is known as a fatal error.
C) This led to the conclusion that the percentage of employees open to new ideas did not increase when in fact it did.
D) This led to the conclusion that the percentage of employees open to new ideas did increase when in fact it did not.
E) This led to a P-value that was greater than the level of significance.

Question 11

Make conclusions about the hypotheses.
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 P-value associated with the test statistic
For testing this claim is 0.0029. At α = .05,

A) we can conclude that the percentage of Americans in these cities experiencing difficulty making mortgage payments is significantly higher than 28%.
B we can conclude that the percentage of Americans in these cities experiencing
Difficulty making mortgage payments is significantly lower than 28%.
C) we can conclude that the percentage of Americans in these cities experiencing difficulty making mortgage payments is not significantly different from 28%.
D) we can conclude that the percentage of Americans in these cities experiencing difficulty making mortgage payments is equal to 28%.
E) None of the above.

Question 12

Find critical values.
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 13

Write the hypotheses.
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 the firm's professionals volunteer an average of more than 15 hours per
Month. 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

Question 14

Calculate the appropriate test statistic.
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

Question 15

Create a confidence interval for the mean difference.
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.
a. Write the null and alternative hypotheses.
b. In this context, describe the Type I error possible. How might such an error impact the company?
c. In this context, describe the Type II error possible. How might such an error impact
the company?
d. 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 16

Calculate the appropriate test statistic.
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 the firm's professionals volunteer an average of more than 15 hours per
Month. If this is not the case, they will institute an incentive program to increase
Community involvement. A random sample of 24 professionals yields a mean of 16.6
Hours and a standard deviation of 2.22 hours. The correct value of the test statistic for the
Appropriate hypothesis test is

Question 17

Create a confidence interval for the mean difference.
Insurance companies track life expectancy information to assist in determining the
cost of life insurance policies. Last year the average life expectancy of all policyholders
was 77 years. ABI Insurance wants to determine if their clients now have a longer life
expectancy, on average, so they randomly sample some of their recently paid policies.

Question 18

Calculate the appropriate test statistic.
Insurance companies track life expectancy information to assist in determining the
Cost of life insurance policies. Last year the average life expectancy of all policyholders
Was 77 years. ABI Insurance wants to determine if their clients now have a longer life
Expectancy, on average, so they randomly sample 20 of their recently paid policies.
The sample has a mean of 78.6 years and a standard deviation of 4.48 years. What is the
Value of the test statistic?

A) 1.896
B) 2.355
C) 1.987
D) 2.176
E) 1.597