Hypothesis Testing (2 samples)
Name _______________________________
Chapter 11 Homework
Read each problem carefully. Write your answer in the blank, or circle the correct answer.
1. Test whether ρ1 > ρ2 at the 0.05 level of significance. Sample data are:
I.
x1 = 127
n1 = 244
x2 = 136
n2 = 313
H0:
H1:
II.
α = 0.05
III.
Test Statistic =
(2 decimals)
IV.
P-value =
(4 decimals)
V.
Reject H0 or Do Not Reject H0
VI.
(fill in the blanks for the conclusion)
There _______________ sufficient evidence to conclude that ______________________________________.
2. In a clinical trial of a vaccine, 8000 children were randomly divided into two groups. The subjects in Group
#1 (the experimental group) were given the vaccine while the subjects in Group #2 (the control group) were
given a placebo. Of the 4000 children in the experimental group, 75 developed the disease. Of the 4000
children in the control group, 118 developed the disease. Determine whether the proportion of subjects in the
experimental group who contracted the disease is LESS than the proportion of subjects in the control group
who contracted the disease. Use α = 0.05.
I.
H0:
H1:
II.
α = 0.05
III.
Test Statistic =
(2 decimals)
IV.
P-value =
(4 decimals)
V.
Reject H0 or Do Not Reject H0
VI.
(fill in the blanks for the conclusion)
There _______________ sufficient evidence to conclude that ______________________________________.
3. Construct a 95% confidence interval for the difference between the two population proportions, ρ1 – ρ2,
for the last example (vaccine). Do not round.
(__________ ,
__________)
Is there a significant difference in the proportions of children who contracted the disease in the two groups?
(yes or no)
4. A survey asked, “How many tattoos do you currently have on your body?” Of the 1216 males surveyed, 195
responded that they had at least one tattoo. Of the 1030 females surveyed, 127 responded that they had at
least one tattoo. Construct a 90% confidence interval to judge whether the proportion of males that have at
least one tattoo differs significantly from the proportion of females that have at least one tattoo.
Do not round.
(__________ ,
__________)
Is there a significant difference in the proportions of men and women who have at least one tattoo?
(yes or no)
5. The following data represent the muzzle velocity (in feet per second) of shells fired from a 155-mm gun.
For each shell, two measurements of velocity were recorded using two different measuring devices.
Observation
Device A
Device B
#1
793.3
793.6
#2
792.8
795.6
#3
793.8
798.4
#4
791.7
798.4
#5
793.2
796
#6
794.9
797.4
Test the claim that there is a difference in the measurements of the muzzle velocity between Device A and B at
the 0.01 level of significance.
I.
H0:
H1:
II.
α = 0.01
III.
Test Statistic =
(2 decimals)
IV.
P-value =
(4 decimals)
V.
Reject H0 or Do Not Reject H0
VI.
(fill in the blanks for the conclusion)
There _______________ sufficient evidence to conclude that ______________________________________.
Construct a 99% confidence interval for the mean difference of the muzzle velocities. Do not round.
(__________ ,
__________)
Is there a significant mean difference in the muzzle velocities? (yes or no)
6. To test the belief that sons are taller than their fathers, a student randomly selects 6 father who have adult
male children. She records the height of both the father and son in inches. The data follow. Test the claim
that sons are taller than their fathers. Use α = 0.10.
Son height
Father height
I.
#1
73
69.6
#2
68.3
66.6
#3
66.5
70.6
#4
67.4
66.8
#5
68.7
72.9
#6
74.9
69.2
H0:
H1:
II.
α = 0.10
III.
Test Statistic =
(2 decimals)
IV.
P-value =
(4 decimals)
V.
Reject H0 or Do Not Reject H0
VI.
(fill in the blanks for the conclusion)
There _______________ sufficient evidence to conclude that ______________________________________.
7. The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being
tested. The manufacturer thinks it might be better to use a diamond indenter so that all types of metal can be
tested. It is suspected that the two methods will produce different hardness readings. The manufacturer uses
both indenters on each specimen and compares the hardness readings. Test the claim that the diamond
reading is lower than the steel-ball reading. Use α = 0.05.
Specimen
Diamond
Steel-Ball
I.
#1
50
52
#2
57
56
#3
61
61
#4
71
74
#5
68
69
#6
54
56
#7
65
68
#8
51
51
#9
53
56
H0:
H1:
II.
α = 0.05
III.
Test Statistic =
(2 decimals)
IV.
P-value =
(4 decimals)
V.
Reject H0 or Do Not Reject H0
VI.
(fill in the blanks for the conclusion)
There _______________ sufficient evidence to conclude that ______________________________________.
Construct a 95% confidence interval for the mean difference of the hardness readings. Do not round.
(__________ ,
__________)
Is there a significant mean difference in the hardness readings?
(yes or no)
8. Test whether µ1 ≠ µ2 using α = 0.01 for the given sample data.
n
I.
x
H0:
s
Population 1
13
18.4
5.3
Population 2
13
25.5
4.5
H1:
II.
α = 0.01
III.
Test Statistic =
(2 decimals)
IV.
P-value =
(4 decimals)
V.
Reject H0 or Do Not Reject H0
VI.
(fill in the blanks for the conclusion)
There _______________ sufficient evidence to conclude that ______________________________________.
Construct a 99% confidence interval for µ1 – µ2. Do not round.
(__________ ,
__________)
Is there a significant difference in the two means?
(yes or no)
9. Test whether µ1 < µ2 using α = 0.05 for the given sample data.
n
I.
H0:
x
s
Population 1
32
103.4
12.2
Population 2
25
114.2
13.3
H1:
II.
α = 0.05
III.
Test Statistic =
(2 decimals)
IV.
P-value =
(4 decimals)
V.
Reject H0 or Do Not Reject H0
VI.
(fill in the blanks for the conclusion)
There _______________ sufficient evidence to conclude that ______________________________________.
10. A study was conducted to determine the effectiveness of a certain treatment. A group of 112 patients
were randomly divided into an experimental group and a control group. The table shows the results of their
improvement.
Experimental
Control
n
61
51
12.2
5.3
x
s
8.5
3.5
Construct a 90% confidence interval for µ1 – µ2. Do not round.
(__________ ,
__________)
Is there a significant difference in the two means?
(yes or no)
11. A researcher wanted to determine if carpeted rooms contain more bacteria than uncarped rooms. The
table shows the resluts for the number of bacteria per cubic foot for both types of rooms. Test the claim that
carpeted rooms contain more bacteria, on average, than uncarpeted rooms using α = 0.01.
Carpeted
11.6
6
6.3
15.1
15.7
11.6
I.
Uncarpeted
13.3
5
7
6
9
11.6
8.9
4.5
9.1
9.3
H0:
H1:
II.
α = 0.01
III.
Test Statistic =
(2 decimals)
IV.
P-value =
(4 decimals)
V.
Reject H0 or Do Not Reject H0
VI.
(fill in the blanks for the conclusion)
There _______________ sufficient evidence to conclude that ______________________________________.