Transcript Chapter 12

Active Learning Lecture Slides
For use with Classroom Response Systems
Chapter 12:
Confidence Intervals and Hypothesis Tests
for Means
Business Statistics
First Edition
by Sharpe, De Veaux, Velleman
Copyright © 2010 Pearson Education, Inc.
Slide 10- 1
Which of the following is not an assumption
or condition that needs to be checked to
construct a confidence interval for the mean
using the Student’s t distribution?
A. Randomization
B. 10% Condition
C. Success/Failure Condition
D. Nearly Normal Condition
Copyright © 2010 Pearson Education, Inc.
Slide 12- 2
Which of the following is not an assumption
or condition that needs to be checked to
construct a confidence interval for the mean
using the Student’s t distribution?
A. Randomization
B. 10% Condition
C. Success/Failure Condition
D. Nearly Normal Condition
Copyright © 2010 Pearson Education, Inc.
Slide 12- 3
Which statement correctly compares t-distributions to
the normal distribution?
I. t distributions and the Normal are symmetric.
II. t distributions have less spread than the Normal
distribution.
III. t distributions and the Normal are bell shaped.
A. I only
B. II only
C. I and II only
D. I and III only
Copyright © 2010 Pearson Education, Inc.
Slide 12- 4
Which statement correctly compares t-distributions to
the normal distribution?
I. t distributions and the Normal are symmetric.
II. t distributions have less spread than the Normal
distribution.
III. t distributions and the Normal are bell shaped.
A. I only
B. II only
C. I and II only
D. I and III only
Copyright © 2010 Pearson Education, Inc.
Slide 12- 5
Which of the following is true about
Student’s t-models?
A. They are unimodal and symmetric.
B. They have fatter tails than the Normal
model.
C. As the degrees of freedom increase, the tmodels look more and more like the Normal
Model
D. All of the above.
Copyright © 2010 Pearson Education, Inc.
Slide 12- 6
Which of the following is true about
Student’s t-models?
A. They are unimodal and symmetric.
B. They have fatter tails than the Normal
model.
C. As the degrees of freedom increase, the tmodels look more and more like the Normal
Model
D. All of the above.
Copyright © 2010 Pearson Education, Inc.
Slide 12- 7
A researcher found that a 98% confidence interval
for the mean hours per week spent studying by
college students was (13, 17). Which is true?
A. There is a 98% chance that the mean hours per
week spent studying by college students is between
13 and 17 hours.
B. We are 98% sure that the mean hours per week
spent studying by college students is between 13
and 17 hours.
C. Students average between 13 and 17 hours per
week studying for 98% of the weeks.
D. 98% of all students spend between 13 and 17
hours studying per week.
Copyright © 2010 Pearson Education, Inc.
Slide 12- 8
A researcher found that a 98% confidence interval
for the mean hours per week spent studying by
college students was (13, 17). Which is true?
A. There is a 98% chance that the mean hours per
week spent studying by college students is between
13 and 17 hours.
B. We are 98% sure that the mean hours per week
spent studying by college students is between 13
and 17 hours.
C. Students average between 13 and 17 hours per
week studying for 98% of the weeks.
D. 98% of all students spend between 13 and 17
hours studying per week.
Copyright © 2010 Pearson Education, Inc.
Slide 12- 9
The owner of small specialty store was interested
in the amount customers spent on designs from a
local artist. From a random sample of 20
customers, she found a mean of $375 with a
standard deviation of $56. To construct a 95%
confidence interval for the true mean amount
spent, she would use a t value of
A. 1.729
B. 2.093
C. 1.96
D. 3.078
Copyright © 2010 Pearson Education, Inc.
Slide 12- 10
The owner of small specialty store was interested
in the amount customers spent on designs from a
local artist. From a random sample of 20
customers, she found a mean of $375 with a
standard deviation of $56. To construct a 95%
confidence interval for the true mean amount
spent, she would use a t value of
A. 1.729
B. 2.093
C. 1.96
D. 3.078
Copyright © 2010 Pearson Education, Inc.
Slide 12- 11
A professor was curious about her students’ grade point
averages (GPAs). She took a random sample of 15 students and
found a mean GPA of 3.01 with a standard deviation of 0.534.
Which of the following formulas gives a 99% confidence interval
for the mean GPA of the professor’s students?
A. 3 .0 1 ± 2 .9 4 7
B. 3 .0 1 ± 2 .9 7 7
0 .5 3 4
15
0 .5 3 4
15
C. 3 .0 1 ± 2 .5 7 6
0 .5 3 4
15
D. 3 .0 1 ± 2 .9 4 7
0 .5 3 4
14
Copyright © 2010 Pearson Education, Inc.
Slide 12- 12
A professor was curious about her students’ grade point
averages (GPAs). She took a random sample of 15 students and
found a mean GPA of 3.01 with a standard deviation of 0.534.
Which of the following formulas gives a 99% confidence interval
for the mean GPA of the professor’s students?
A. 3 .0 1 ± 2 .9 4 7
B. 3 .0 1 ± 2 .9 7 7
0 .5 3 4
15
0 .5 3 4
15
C. 3 .0 1 ± 2 .5 7 6
0 .5 3 4
15
D. 3 .0 1 ± 2 .9 4 7
0 .5 3 4
14
Copyright © 2010 Pearson Education, Inc.
Slide 12- 13
A coffee house owner knows that customers pour different
amounts of coffee into their cups. She samples cups from 10
costumers she believes to be representative of the customers
and weighs the cups, finding a mean of 12.5 ounces and
standard deviation of 0.5 ounces. Which of the following
formulas gives a 95% confidence interval for the mean weight of
all cups of coffee?
A. 1 2 .5 ± 1 .9 6
0 .5
10
B. 1 2 .5 ± 2 , 2 2 8
0 .5
10
C.
1 2 .5 ± 2 .2 6 2
D. 1 2 .5 ± 2 .2 6 2
0 .5
10
0 .5
9
Copyright © 2010 Pearson Education, Inc.
Slide 12- 14
A coffee house owner knows that customers pour different
amounts of coffee into their cups. She samples cups from 10
costumers she believes to be representative of the customers
and weighs the cups, finding a mean of 12.5 ounces and
standard deviation of 0.5 ounces. Which of the following
formulas gives a 95% confidence interval for the mean weight of
all cups of coffee?
A. 1 2 .5 ± 1 .9 6
0 .5
10
B. 1 2 .5 ± 2 , 2 2 8
0 .5
10
C.
1 2 .5 ± 2 .2 6 2
D. 1 2 .5 ± 2 .2 6 2
0 .5
10
0 .5
9
Copyright © 2010 Pearson Education, Inc.
Slide 12- 15
After instituting some improvements, a bank wished
to test whether service times at the drive through
window improved. The average service time had
been 110 seconds. A sample of 25 customers
resulted in a mean of 100 seconds with a standard
deviation of 40 seconds. Which hypotheses should
they test?
A. H0: µ < 110 HA: µ > 110
B. H0: µ = 110 HA: µ > 110
C. H0: µ > 100 HA: µ = 100
D. H0: µ = 110 HA: µ < 110
Copyright © 2010 Pearson Education, Inc.
Slide 11- 16
After instituting some improvements, a bank wished
to test whether service times at the drive through
window improved. The average service time had
been 110 seconds. A sample of 25 customers
resulted in a mean of 100 seconds with a standard
deviation of 40 seconds. Which hypotheses should
they test?
A. H0: µ < 110 HA: µ > 110
B. H0: µ = 110 HA: µ > 110
C. H0: µ > 100 HA: µ = 100
D. H0: µ = 110 HA: µ < 110
Copyright © 2010 Pearson Education, Inc.
Slide 11- 17
After instituting some improvements, a bank wished
to test whether service times at the drive through
window improved. The average service time had
been 110 seconds. A sample of 25 customers
resulted in a mean of 100 seconds with a standard
deviation of 40 seconds. What is the value of the
calculated t statistic?
A. -1.25
B. 0.25
C. 2.75
D. -2.35
Copyright © 2010 Pearson Education, Inc.
Slide 11- 18
After instituting some improvements, a bank wished
to test whether service times at the drive through
window improved. The average service time had
been 110 seconds. A sample of 25 customers
resulted in a mean of 100 seconds with a standard
deviation of 40 seconds. What is the value of the
calculated t statistic?
A. -1.25
B. 0.25
C. 2.75
D. -2.35
Copyright © 2010 Pearson Education, Inc.
Slide 11- 19
After instituting some improvements, a bank wished
to test whether service times at the drive through
window improved. The average service time had
been 110 seconds. A sample of 25 customers
resulted in a mean of 100 seconds with a standard
deviation of 40 seconds. What can we conclude?
A. The mean service time increased.
B. The mean service time did not decrease.
C. The test is inconclusive.
D. The mean service time decreased.
Copyright © 2010 Pearson Education, Inc.
Slide 11- 20
After instituting some improvements, a bank wished
to test whether service times at the drive through
window improved. The average service time had
been 110 seconds. A sample of 25 customers
resulted in a mean of 100 seconds with a standard
deviation of 40 seconds. What can we conclude?
A. The mean service time increased.
B. The mean service time did not decrease.
C. The test is inconclusive.
D. The mean service time decreased.
Copyright © 2010 Pearson Education, Inc.
Slide 11- 21