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Chapter 11:
Testing Hypothesis About Proportions
Business Statistics
First Edition
by Sharpe, De Veaux, Velleman
Copyright © 2010 Pearson Education, Inc.
Slide 10- 1
A P-value for a hypothesis test 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.
Copyright © 2010 Pearson Education, Inc.
Slide 11- 2
A P-value for a hypothesis test 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.
Copyright © 2010 Pearson Education, Inc.
Slide 11- 3
A small P-value indicates either that the
observation is improbable or that the
probability calculation was based on
incorrect assumptions.
A. True
B. False
Copyright © 2010 Pearson Education, Inc.
Slide 11- 4
A small P-value indicates either that the
observation is improbable or that the
probability calculation was based on
incorrect assumptions.
A. True
B. False
Copyright © 2010 Pearson Education, Inc.
Slide 11- 5
In a hypothesis test, the null hypothesis
typically represents the status quo.
A. True
B. False
Copyright © 2010 Pearson Education, Inc.
Slide 11- 6
In a hypothesis test, the null hypothesis
typically represents the status quo.
A. True
B. False
Copyright © 2010 Pearson Education, Inc.
Slide 11- 7
According to a June 2004 Gallup poll, 28% of
Americans experienced times when they haven’t
been able to afford medical care. Is this proportion
higher for black Americans than for all Americans?
In a random sample of 801 black Americans, 38%
reported that there had been times in the last year
when they had not been able to afford medical care.
Which type of hypothesis test would you use?
A. One-tail upper tail
B. One-tail lower tail
C. Two-tail
D. Both A and B
Copyright © 2010 Pearson Education, Inc.
Slide 11- 8
According to a June 2004 Gallup poll, 28% of
Americans experienced times when they haven’t
been able to afford medical care. Is this proportion
higher for black Americans than for all Americans?
In a random sample of 801 black Americans, 38%
reported that there had been times in the last year
when they had not been able to afford medical care.
Which type of hypothesis test would you use?
A. One-tail upper tail
B. One-tail lower tail
C. Two-tail
D. Both A and B
Copyright © 2010 Pearson Education, Inc.
Slide 11- 9
A statistics professor wants to see if more than 80%
of her students enjoyed taking her class. At the end
of the term she surveys a random sample of students
from her large class. Which set of hypotheses
should she test?
A. H0: p < 0.80 HA: p > 0.80
B. H0: p = 0.80 HA: p > 0.80
C. H0: p > 0.80 HA: p = 0.80
D. H0: p = 0.80 HA: p < 0.80
Copyright © 2010 Pearson Education, Inc.
Slide 11- 10
A statistics professor wants to see if more than 80%
of her students enjoyed taking her class. At the end
of the term she surveys a random sample of students
from her large class. Which set of hypotheses
should she test?
A. H0: p < 0.80 HA: p > 0.80
B. H0: p = 0.80 HA: p > 0.80
C. H0: p > 0.80 HA: p = 0.80
D. H0: p = 0.80 HA: p < 0.80
Copyright © 2010 Pearson Education, Inc.
Slide 11- 11
After collecting data from her class, the statistics
professor calculates a z statistic of 2.69. Which of
the following is true?
A. The P-value is .9964 and conclude that more than
80% of the students enjoyed her class.
B. The P-value is .0036 and conclude that more than
80% of the students enjoyed her class.
C. The P-value is .9964 and conclude that less than
80% of the students enjoyed her class.
D. The P-value is .0036 and conclude that less than
80% of the students enjoyed her class.
Copyright © 2010 Pearson Education, Inc.
Slide 11- 12
After collecting data from her class, the statistics
professor calculates a z statistic of 2.69. Which of
the following is true?
A. The P-value is .9964 and conclude that more than
80% of the students enjoyed her class.
B. The P-value is .0036 and conclude that more than
80% of the students enjoyed her class.
C. The P-value is .9964 and conclude that less than
80% of the students enjoyed her class.
D. The P-value is .0036 and conclude that less than
80% of the students enjoyed her class.
Copyright © 2010 Pearson Education, Inc.
Slide 11- 13
An online catalog company wants on-time delivery
for at least 90% of the orders they ship. They have
been shipping orders via UPS and FedEx but is
considering a new, cheaper delivery service
(ShipFast). The company sends a random sample of
orders via ShipFast, and then makes follow-up phone
calls to see if these orders arrived on time. To test if
ShipFast meets their requirements, which
hypotheses should they test?
A. H0: p < 0.90 HA: p > 0.90
B. H0: p = 0.90 HA: p > 0.90
C. H0: p > 0.90 HA: p = 0.90
D. H0: p = 0.90 HA: p < 0.90
Copyright © 2010 Pearson Education, Inc.
Slide 11- 14
An online catalog company wants on-time delivery
for at least 90% of the orders they ship. They have
been shipping orders via UPS and FedEx but is
considering a new, cheaper delivery service
(ShipFast). The company sends a random sample of
orders via ShipFast, and then makes follow-up phone
calls to see if these orders arrived on time. To test if
ShipFast meets their requirements, which
hypotheses should they test?
A. H0: p < 0.90 HA: p > 0.90
B. H0: p = 0.90 HA: p > 0.90
C. H0: p > 0.90 HA: p = 0.90
D. H0: p = 0.90 HA: p < 0.90
Copyright © 2010 Pearson Education, Inc.
Slide 11- 15
Based on sample data, the online catalog company considering
ShipFast conducts the hypothesis test and calculates a z
statistic of 2.15. Which of the following is true?
A. The P-value is 0.0158 so we conclude that ShipFast meets
the company’s requirements for on-time delivery.
B. The P-value is .9842 so we conclude that ShipFast meets the
company’s requirements for on-time delivery.
C. The P-value is 0.0158 so we conclude that ShipFast does not
meet the company’s requirements for on-time delivery.
D. The P-value is .9842 so we conclude that ShipFast does not
meet the company’s requirements for on-time delivery.
Copyright © 2010 Pearson Education, Inc.
Slide 11- 16
Based on sample data, the online catalog company considering
ShipFast conducts the hypothesis test and calculates a z
statistic of 2.15. Which of the following is true?
A. The P-value is 0.0158 so we conclude that ShipFast meets
the company’s requirements for on-time delivery.
B. The P-value is .9842 so we conclude that ShipFast meets the
company’s requirements for on-time delivery.
C. The P-value is 0.0158 so we conclude that ShipFast does not
meet the company’s requirements for on-time delivery.
D. The P-value is .9842 so we conclude that ShipFast does not
meet the company’s requirements for on-time delivery.
Copyright © 2010 Pearson Education, Inc.
Slide 11- 17
The threshold for a P-value that determines
when we reject a null hypothesis is called the
A. alpha level.
B. power.
C. beta level.
D. confidence level.
Copyright © 2010 Pearson Education, Inc.
Slide 11- 18
The threshold for a P-value that determines
when we reject a null hypothesis is called the
A. alpha level.
B. power.
C. beta level.
D. confidence level.
Copyright © 2010 Pearson Education, Inc.
Slide 11- 19
We commit a Type II error when we reject the
null hypothesis when it is true.
A. True
B. False
Copyright © 2010 Pearson Education, Inc.
Slide 11- 20
We commit a Type II error when we reject the
null hypothesis when it is true.
A. True
B. False
Copyright © 2010 Pearson Education, Inc.
Slide 11- 21