Transcript chapter_10_powerpoint

Chapter 10
t Tests, Two-Way Tables,
and ANOVA
Active Learning
Questions
For use with classroom
response systems
Copyright © 2009 Pearson Education, Inc.
Slide 10 - 1
This partial
t-table can be
used where
necessary.
Slide 10 - 2
The t distribution can be used when finding a
confidence interval for the population mean with a
small sample whenever the sample comes from a
symmetric population.
a. True
b. False
Slide 10 - 3
The t distribution can be used when finding a
confidence interval for the population mean with a
small sample whenever the sample comes from a
symmetric population.
a. True
b. False
Slide 10 - 4
A simple random sample from a normal
distribution is taken in order to obtain a 95%
confidence interval for the population mean. If the
sample size is 12, the sample mean x is 32, and the
sample standard deviation s is 9.5, what is the
margin of error?
a. 0.604
b. 1.74
c. 5.98
d. 6.04
Slide 10 - 5
A simple random sample from a normal
distribution is taken in order to obtain a 95%
confidence interval for the population mean. If the
sample size is 12, the sample mean x is 32, and the
sample standard deviation s is 9.5, what is the
margin of error?
a. 0.604
b. 1.74
c. 5.98
d. 6.04
Slide 10 - 6
A 95% confidence interval for the mean of a
normal population is found to be 17.6 <  < 20.8.
What is the margin of error?
a. 0.8
b. 0.16
c. 1.6
d. 16
Slide 10 - 7
A 95% confidence interval for the mean of a
normal population is found to be 17.6 <  < 20.8.
What is the margin of error?
a. 0.8
b. 0.16
c. 1.6
d. 16
Slide 10 - 8
The margin of error in estimating the population
mean of a normal population is E = 9.3 when the
sample size is 15. If the sample size had been 6
and the sample standard deviation did not change,
how would the margin of error change?
a. It would be smaller
b. It would be larger
c. It would stay the same
d. Cannot be determined
Slide 10 - 9
The margin of error in estimating the population
mean of a normal population is E = 9.3 when the
sample size is 15. If the sample size had been 6
and the sample standard deviation did not change,
how would the margin of error change?
a. It would be smaller
b. It would be larger
c. It would stay the same
d. Cannot be determined
Slide 10 - 10
A golfer wished to find a ball that would travel
more than 200 yards when hit with his 4-iron with
a club speed of 90 miles per hour. He had a golf
equipment lab test a low compression ball by
having a robot swing his club 9 times at the
required speed. State the null and alternative
hypotheses for this test.
a. H0:  = 200; Ha:  < 200
b. H0:  ≥ 200; Ha:  < 200
c. H0:  = 200; Ha:  > 200
d. H0:  ≤ 200; Ha:  > 200
Slide 10 - 11
A golfer wished to find a ball that would travel
more than 200 yards when hit with his 4-iron with
a club speed of 90 miles per hour. He had a golf
equipment lab test a low compression ball by
having a robot swing his club 9 times at the
required speed. State the null and alternative
hypotheses for this test.
a. H0:  = 200; Ha:  < 200
b. H0:  ≥ 200; Ha:  < 200
c. H0:  = 200; Ha:  > 200
d. H0:  ≤ 200; Ha:  > 200
Slide 10 - 12
Data from the test in the previous example resulted
in a sample mean of 206.8 yards with a sample
standard deviation of 4.6 yards. Assuming
normality, find the value of the t statistic. Recall
the mean being tested was 200 yards with 9
swings by the robot.
a. –4.435
b. –13.304
c. 4.435
d. 13.304
Slide 10 - 13
Data from the test in the previous example resulted
in a sample mean of 206.8 yards with a sample
standard deviation of 4.6 yards. Assuming
normality, find the value of the t statistic. Recall
the mean being tested was 200 yards with 9
swings by the robot.
a. –4.435
b. –13.304
c. 4.435
d. 13.304
Slide 10 - 14
Data from the test in the previous example resulted
in a sample mean of 206.8 yards with a sample
standard deviation of 4.6 yards. Assuming
normality, find the critical value at the 0.05
significance level. Recall the mean being tested
was 200 yards with 9 swings by the robot.
a. 2.306
b. 2.262
c. 1.833
d. 1.860
Slide 10 - 15
Data from the test in the previous example resulted
in a sample mean of 206.8 yards with a sample
standard deviation of 4.6 yards. Assuming
normality, find the critical value at the 0.05
significance level. Recall the mean being tested
was 200 yards with 9 swings by the robot.
a. 2.306
b. 2.262
c. 1.833
d. 1.860
Slide 10 - 16
For the previous example, determine the results of
a hypothesis test.
a.
b.
c.
d.
Reject the null hypothesis. The data provide
sufficient evidence that the average distance is
greater than 200 yards.
Accept the null hypothesis. The data provide
sufficient evidence that the average distance is
greater than 200 yards.
Reject the null hypothesis. The data do not provide
sufficient evidence that the average distance is
greater than 200 yards.
Accept the null hypothesis. The data do not provide
sufficient evidence that the average distance is
greater than 200 yards.
Slide 10 - 17
For the previous example, determine the results of
a hypothesis test.
a.
b.
c.
d.
Reject the null hypothesis. The data provide
sufficient evidence that the average distance is
greater than 200 yards.
Accept the null hypothesis. The data provide
sufficient evidence that the average distance is
greater than 200 yards.
Reject the null hypothesis. The data do not provide
sufficient evidence that the average distance is
greater than 200 yards.
Accept the null hypothesis. The data do not provide
sufficient evidence that the average distance is
greater than 200 yards.
Slide 10 - 18
One hundred people are selected at random and tested
for colorblindness to determine whether gender and
colorblindness are independent. The following counts
were observed. Find the expected value of a male who is
not colorblind.
Colorblind Not Colorblind Total
Male
9
51
60
Female
1
39
40
Total
10
90
100
a. 6.0
b. 54.0
c. 4.0
d. 36.0
Slide 10 - 19
One hundred people are selected at random and tested
for colorblindness to determine whether gender and
colorblindness are independent. The following counts
were observed. Find the expected value of a male who is
not colorblind.
Colorblind Not Colorblind Total
Male
9
51
60
Female
1
39
40
Total
10
90
100
a. 6.0
b. 54.0
c. 4.0
d. 36.0
Slide 10 - 20
For the previous example, here are the expected
values. Find the value of the 2 statistic.
Colorblind Not Colorblind Total
Male
6.0
54.0
60
Female
4.0
36.0
40
Total
10.0
90.0
100
a. 1.389
b. 1.0
c. 4.167
d. 4.0
Slide 10 - 21
For the previous example, here are the expected
values. Find the value of the 2 statistic.
Colorblind Not Colorblind Total
Male
6.0
54.0
60
Female
4.0
36.0
40
Total
10.0
90.0
100
a. 1.389
b. 1.0
c. 4.167
d. 4.0
Slide 10 - 22
State the null and alternative hypothesis for the
test associated with the data in the previous
example.
a. H0: Colorblindness and gender are independent
Ha: Colorblindness and gender are related
b. H0: Colorblindness and gender are dependent
Ha: Colorblindness and gender are not related
c. H0: Colorblindness and gender are related
Ha: Colorblindness and gender are independent
d. H0: Colorblindness and gender are nor related
Ha: Colorblindness and gender are dependent
Slide 10 - 23
State the null and alternative hypothesis for the
test associated with the data in the previous
example.
a. H0: Colorblindness and gender are independent
Ha: Colorblindness and gender are related
b. H0: Colorblindness and gender are dependent
Ha: Colorblindness and gender are not related
c. H0: Colorblindness and gender are related
Ha: Colorblindness and gender are independent
d. H0: Colorblindness and gender are nor related
Ha: Colorblindness and gender are dependent
Slide 10 - 24
The critical value of 2 for a 2 x 2 table using a
0.05 significance level is 3.841. If the value of the
2 statistic in the previous example had been
4.216, state your conclusion about the relationship
between gender and colorblindness.
a. Reject H0. There is insufficient evidence to support the
claim that colorblindness and gender are related.
b. Accept H0. There is insufficient evidence to support the
claim that colorblindness and gender are related.
c. Reject H0. There is sufficient evidence to support the claim
that colorblindness and gender are related.
d. Accept H0. There is sufficient evidence to support the claim
that colorblindness and gender are related.
Slide 10 - 25
The critical value of 2 for a 2 x 2 table using a
0.05 significance level is 3.841. If the value of the
2 statistic in the previous example had been
4.216, state your conclusion about the relationship
between gender and colorblindness.
a. Reject H0. There is insufficient evidence to support the
claim that colorblindness and gender are related.
b. Accept H0. There is insufficient evidence to support the
claim that colorblindness and gender are related.
c. Reject H0. There is sufficient evidence to support the claim
that colorblindness and gender are related.
d. Accept H0. There is sufficient evidence to support the claim
that colorblindness and gender are related.
Slide 10 - 26
The data given were
analyzed using one-way
analysis or variance. The
purpose of the analysis
is to:
A
29
26
25
28
B
27
23
29
21
C
19
21
25
17
a. determine whether the groups A, B, and C are
independent.
b. test the hypothesis that the population means of the
three groups are equal.
c. test the hypothesis that the population variances of
the three groups are equal.
d. test the hypothesis that the sample means of the
three groups are equal.
Slide 10 - 27
The data given were
analyzed using one-way
analysis or variance. The
purpose of the analysis
is to:
A
29
26
25
28
B
27
23
29
21
C
19
21
25
17
a. determine whether the groups A, B, and C are
independent.
b. test the hypothesis that the population means of the
three groups are equal.
c. test the hypothesis that the population variances of
the three groups are equal.
d. test the hypothesis that the sample means of the
three groups are equal.
Slide 10 - 28
Here are the results of the ANOVA for the
previous example (question on next slide):
SUMMARY
Groups
Count
A
4
B
4
C
4
SUMMARY
Source of Variation
Between Groups
Within Groups
Total
Sums
108
100
Average Variance
27 3.33333
25 13.33333
82
20.5 11.66667
SS df MS
88.7 2 44.3
85 9
173.7 11
F P-value
F crit
4.694 0.0401 4.25649
9.4
Slide 10 - 29
If the significance level for the test is 0.05, which
conclusion below is correct?
a. The data do not provide sufficient evidence to conclude
that the population means of groups A, B, and C are
related.
b. The data do not provide sufficient evidence to conclude
that the population means of groups A, B, and C are
different.
c. The data do not provide sufficient evidence to conclude
that the population variances of groups A, B, and C are
different.
d. The data do not provide sufficient evidence to conclude
that the population means of groups A, B, and C are
different.
Slide 10 - 30
If the significance level for the test is 0.05, which
conclusion below is correct?
a. The data do not provide sufficient evidence to conclude
that the population means of groups A, B, and C are
related.
b. The data do not provide sufficient evidence to conclude
that the population means of groups A, B, and C are
different.
c. The data do not provide sufficient evidence to conclude
that the population variances of groups A, B, and C are
different.
d. The data do not provide sufficient evidence to conclude
that the population means of groups A, B, and C are
different.
Slide 10 - 31