IIIA-1
Business Statistics: Part III: Inference for Decision Making – Test A
Name___________________________________________________
Chapter 10: Write null and alternative hypotheses.
1. A truck company wants on-time delivery for 98% of the parts they order from a metal
manufacturing plant. They have been ordering from Hudson Manufacturing but will
switch to a new, cheaper manufacturer (Steel-R-Us) unless there is evidence that this
new manufacturer cannot meet the 98% on-time goal. As a test the truck company
purchases a random sample of metal parts from Steel-R-Us, and then determines if
these parts were delivered on-time. Which hypotheses should they test?
A. 0:0.98
:0.98
a
Hp
Hp
<
>
B. 0:0.98
:0.98
a
Hp
Hp
>
=
C. 0:0.98
:0.98
a
Hp
Hp
=
<
D. 0:0.98
:0.98
a
Hp
Hp
=
≠
E. 0:0.98
:0.98
a
Hp
Hp
=
>
Chapter 11: Perform hypothesis tests for means.
2. The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A
random sample of 15 patties yields a mean weight of 3.8 ounces with a sample standard
deviation of 0.5 ounces. At the 0.05 level of significance, perform a hypothesis test to
see if the true mean weight is less than 4 ounces.
The correct null and alternative hypotheses are
A. H0 : µ = 4; HA : µ > 4
B. H0 : µ = 4; HA : µ < 4
C. H0 : µ > 4; HA : µ = 4
D. H0 : µ < 4; HA : µ = 4
E. H0 : µ = 4; HA : µ ≠ 4
IIIA-2 Part III: Inference for Decision Making
Chapter 11: Perform hypothesis tests for means.
3. The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A
random sample of 15 patties yields a mean weight of 3.8 ounces with a sample standard
deviation of 0.5 ounces. At the .05 level of significance, perform a hypothesis test to see
if the true mean weight is less than 4 ounces.
The correct calculated value of the test statistic is
A. -0.4
B. 0.4
C. -1.55
D. 1.55
E. 2.79
Chapter 12: Investigate and interpret P‐values in the context of t‐tests.
4. A sample of 30 year fixed mortgage rates at 12 randomly chosen credit unions yields a
mean rate of 6.65 % and a sample standard deviation of 0.38%. A sample of 30 year
fixed mortgage rates at 16 randomly selected banks yields a mean rate of 7.05% and a
sample standard deviation of 0.22%. Are the mean rates different between credit unions
and banks? Relevant output is shown below. At the 0.05 level of significance, the
correct conclusion is
Two-Sample T-Test and CI
Sample N Mean StDev SE Mean
1 12 6.650 0.390 0.11
2 16 7.050 0.220 0.055
Difference = mu (1) – mu (2)
Estimate for difference: -0.400
95% CI for difference: (-0.666, -0.134)
T-Test of difference = 0 (vs not =): T-Value = -3.19 P-Value = 0.006 DF = 16
A. Reject the null hypothesis.
B. Do not reject the null hypothesis.
C. Evidence suggests that there is a significant difference in mean mortgage rates
between credit unions and banks.
D. Both A and C.
E. Both B and C.
Chapter 10: Interpret and understand P‐values and alpha levels.
5. A P-value indicates
A. the probability that the null hypothesis is true.
B. the probability that the alternative hypothesis is true.
C. the probability of the observed statistic given that the null hypothesis is true.
D. the probability of the observed statistic given that the alternative hypothesis is
true.
E. None of the above.
Test A IIIA-3
Chapter 12: Investigate and interpret P‐values in the context of t‐tests.
6. A professor was interested in determining whether the prices of new textbooks in the
bookstore were higher than if purchased online. She selected 6 textbooks and priced each
at the bookstore and online.
Paired T for Bookstore – Online
N Mean StDev SE Mean
Bookstore 6 115.00 22.36 9.13
Online 6 105.83 13.20 5.39
Difference 6 9.17 13.20 5.39
95% lower bound for mean difference: -1.69
T-Test of mean difference = 0 (vs > 0): T-Value = 1.70 P-Value = 0.075
Based on her analysis, we can conclude at the 0.05 level of significance that
A. The prices are the same in the bookstore and online.
B. The prices are higher in the bookstore.
C. The prices are higher online.
D. The prices are different in the bookstore and online.
E. The analysis is not conclusive.
Chapter 10: Identify and understand Type I errors, Type II errors, and the power of a test.
7. Absorption rates into the body are important considerations when manufacturing a
generic version of a brand-name drug. A pharmacist read that the absorption rate into
the body of a new generic drug (G) is the same as its brand-name counterpart (B). She
has a researcher friend of hers run a small experiment to test 0
H: 0
GB
−=
μμ
against the
alternative H : 0
AG B
−≠
μμ
. Which of the following would be a Type I error?
A. Deciding that the absorption rates are the same, when in fact they are.
B. Deciding that the absorption rates are different, when in fact they are.
C. Deciding that the absorption rates are the same, when in fact they are not.
D. Deciding that the absorption rates are different, when in fact they are not.
E. The researcher cannot make a Type I error, since he has run an experiment.
Chapter 11: Create and interpret confidence intervals for the mean.
8. We have created a 95% confidence interval for µ with the result (10, 15). What
conclusion will we make if we test 0
H : µ = 16 versus HA : µ ≠ 16 at α = 0.05?
A. Reject the null hypothesis
B. Accept the null hypothesis
C. Fail to reject the null hypothesis.
D. Reject the alternative hypothesis.
E. No decision can be made from the information given.
IIIA-4 Part III: Inference for Decision Making
Chapter 10: Understand errors in hypothesis tests.
9. Suppose that a manufacturer is testing one of its machines to make sure that the
machine is producing more than 97% good parts
()
0A
H : 0.97 and H : 0.97pp=>.
The test results in a P-value of 0.102. In reality, the machine is producing 99% good
parts. What probably happens as a result of our testing?
A. We correctly fail to reject 0
H.
B. We correctly reject 0
H.
C. We reject
0
H, making a Type I error.
D. We fail to reject 0
H, making a Type I error.
E. We fail to reject 0
H, making a Type II error.
Chapter 10: Perform hypothesis tests for means.
10. The weights of soy patties sold by Veggie Burgers Delight are normally distributed.
A random sample of 15 patties yields a mean weight of 3.8 ounces with a sample
standard deviation of 0.5 ounces. At the 0.05 level of significance, perform a hypothesis
test to see if the true mean weight is less than 4 ounces.
The correct conclusion at the 0.05 level of significance is
A. Do not reject the null hypothesis.
B. Reject the null hypothesis.
C. Evidence suggests that the mean weight is less than 4 ounces.
D. Both A and C.
E. Both B and C.
Chapter 12: Determine whether two samples are independent or paired.
11. A sample of 30 year fixed mortgage rates at 12 randomly chosen credit unions yields
a mean rate of 6.65 % and a sample standard deviation of 0.38%. A sample of 30 year
fixed mortgage rates at 16 randomly selected banks yields a mean rate of 7.05% and a
sample standard deviation of 0.22%. Are the mean rates different between credit unions
and banks? Relevant output is shown below. Which of the following is true?
Sample N Mean StDev SE Mean
1 12 6.650 0.390 0.11
2 16 7.050 0.220 0.055
Difference = mu (1) – mu (2)
Estimate for difference: -0.400
95% CI for difference: (-0.666, -0.134)
T-Test of difference = 0 (vs not =): T-Value = -3.19 P-Value = 0.006 DF = 16
A. This is a paired design.
B. This is a test of two means from independent samples.
C. This is a one tailed test.
D. Both A and C.
E. Both B and C.
Test A IIIA-5
Chapter 12: Determine whether two samples are independent or paired.
12. Which of the following is not an assumption or condition that needs to be checked
for a paired t-interval?
A. Paired Data
B. Independent Groups
C. Randomization
D. 10% Condition
E. Nearly Normal Condition
Chapter 13: Perform tests for goodness‐of‐fit, homogeneity, or independence.
13. Chris Columbus is responsible for controlling inventory levels for four types of
sailboats sold by his company. Chris takes a sample of 48 boats sold over the past
several months to determine if demand is the same for each type. His results are as
follows:
Type of Boat Sales
Pirate’s Revenge 15
Jolly Roger 11
Sails Delight 10
Cruiser Cove 12
The correct null hypothesis to be tested is
A. Type of boat and demand are related.
B. The demand differs for each type of boat.
C. The demand is the same for each type of boat.
D. Both A and B.
E. Both A and C.
Chapter 13: Perform tests for goodness‐of‐fit, homogeneity, or independence.
14. Chris Columbus is responsible for controlling inventory levels for four types of
sailboats sold by his company. Chris takes a sample of 48 boats sold over the past
several months to determine if demand is the same for each type. His results are as
follows:
Type of Boat Sales
Pirate’s Revenge 15
Jolly Roger 11
Sails Delight 10
Cruiser Cove 12
The calculated value of the Chi Square statistic is
A. 7.815
B. 1.17
C. 22.35
D. -1.17
E. 12.56
IIIA-6 Part III: Inference for Decision Making
Chapter 13: Perform tests for goodness‐of‐fit, homogeneity, or independence.
15. Chris Columbus is responsible for controlling inventory levels for four types of
sailboats sold by his company. Chris takes a sample of 48 boats sold over the past
several months to determine if demand is the same for each type. His results are as
follows:
Type of Boat Sales
Pirate’s Revenge 15
Jolly Roger 11
Sails Delight 10
Cruiser Cove 12
At the 0.05 level of significance, the correct conclusion is
A. Evidence suggests that the demand is the same for different types of boats.
B. Evidence suggests that the demand is not the same for different types of boats.
C. Reject the null hypothesis.
D. Both A and C.
E. Both B and C.
Chapter 11: Perform hypothesis tests for means.
16. A manufacturer of cordless electric shavers sampled 13 from a day’s production and
found the mean time of continuous usage without recharging to be 410 minutes with a
sample standard deviation of 30 minutes. We can assume that times are normally
distributed. We wish to test if the true mean operating time without recharging is more
than 400 minutes. The correct null and alternative hypotheses are
A. H0 : µ = 400; HA : µ < 400
B. H0 : µ = 400; HA : µ > 400
C. H0 : µ > 400; HA : µ = 400
D. H0 : µ < 400; HA : µ = 400
E. H0 : µ = 400; HA : µ ≠ 400
Chapter 11: Perform hypothesis tests for means.
17. A manufacturer of cordless electric shavers sampled 13 from a day’s production and
found the mean time of continuous usage without recharging to be 410 minutes with a
sample standard deviation of 30 minutes. We can assume that times are normally
distributed. We wish to test if the true mean operating time without recharging is more
than 400 minutes. The correct calculated value of the test statistic is
A. 1.20
B. -0.333
C. -2.52
D. -1.20
E. 2.79
Test A IIIA-7
Chapter 10: Make Interpret and understand P‐values and alpha levels.
18. A manufacturer of cordless electric shavers sampled 13 from a day’s production and
found the mean time of continuous usage without recharging to be 410 minutes with a
sample standard deviation of 30 minutes. We can assume that times are normally
distributed. We wish to test if the true mean operating time without recharging is more
than 400 minutes. The correct conclusion at the 0.05 level of significance is
A. Reject the null hypothesis.
B. Do not reject the null hypothesis.
C. Evidence suggests that the mean operating time is more than 400 minutes.
D. Both A and C.
E. Both B and C.
Chapter 12: Construct and interpret a confidence interval for a two‐sample t‐test.
19. An urban planning group is interested in estimating the difference in mean household
income between two neighborhoods. They obtain the following 95% confidence
interval: 95% CI for difference: (-5693, -4107). Which of the following is true?
A. This is a paired design.
B. There is no significant difference in the mean household incomes between the two
neighborhoods at α = 0.05.
C. There is a significant difference in the mean household incomes between the two
neighborhoods at α = 0.05.
D. Both A and B.
E. Both A and C.
Chapter 13: Analyze conclusions using standardized residuals.
20. The residual, or the difference, between the observed frequency and the expected
frequency is a reliable indicator. A standardized residual can also be computed for each
cell. Which statements are true about standardized residuals?
A. Standardized residuals that have a positive value mean that the cell was over-
represented in the actual sample, compared to the expected frequency.
B. The standardized residual can be compared against the critical z-value for your α
level to determine significance.
C. Standardized residuals can be used to test the null hypothesis that the actual
frequency equals the expected frequency for a specific cell versus the research
hypothesis of a difference greater than zero.
D. Standardized residuals that have a negative value mean that the cell was under-
represented in the actual sample, compared to the expected frequency.
E. All of the above.
IIIA-8 Part III: Inference for Decision Making
Business Statistics: Part III: Inference for Decision Making – Test A – Key