Deck 10: Testing Hypotheses About Proportions

Question 1

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

Answer 1

E

Question 2

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

Answer 2

B

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

A

Question 4

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.

Question 5

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 6

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 7

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)

Question 8

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
D)Both A and C
E)Both B and C

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? The correct null and alternative hypotheses
For testing this claim are

Question 10

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
B)we can conclude that the percentage of Americans in these cities experiencing
C)we can conclude that the percentage of Americans in these cities experiencing
D)we can conclude that the percentage of Americans in these cities experiencing
E)None of the above.

Question 11

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

A)t = 3.532
B)t = -3.532
C)t = 1.223
D)t = -1.223
E)t = 0.789

Question 12

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
D)This led to the conclusion that the percentage of employees open to new ideas did
E)This led to a P-value that was greater than the level of significance.

Question 13

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 10.8.Identify and interpret types of error.

Question 14

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 10.6.Calculate the appropriate test statistic.

Question 15

You have determined that your cutoff value at a level  = 0.05 is 1.645 when testing for the mean of a population.If you calculate a test statistic of 1.8, 10.8.Find critical values.

Question 16

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
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.