2018. 7. 25.
Homework 7 Chapter 7-YoonJee Choi
Instructor: Norly GERMAIN
Course: MATH2001: Statistics PB1
40427
Student: YoonJee Choi
Date: 07/25/18
Assignment: Homework 7 Chapter 7
1. What are the two types of hypotheses used in a hypothesis test? How are they related?
What are the two types of hypotheses used in a hypothesis test?
lefttailed and righttailed
null and alternative
type I and type II
population and sample
How are they related?
One is a subset of the other.
They are complements.
They sum to zero.
They are equal.
2. What are the two decisions that you can make from performing a hypothesis test?
What are the two decisions that you can make from performing a hypothesis test? Select all that apply.
A. accept the alternative hypothesis
B. reject the alternative hypothesis
C. reject the null hypothesis
D. accept the null hypothesis
E. make a type II error
F.
G. fail to reject the null hypothesis
H. make a type I error
fail to reject the alternative hypothesis
3. Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha.
μ
≥ 464
Find the complement of the claim.
μ
(1)
464
Which is H0 and which is Ha?
(1)
A. H0 : μ ≤ 464
Ha: μ ≥ 464
B. H0 : μ ≥ 464
Ha: μ = 464
C. H0 : μ ≥ 464
Ha: μ < 464
D. H0 : μ ≥ 464
Ha: μ ≠ 464
E. H0 : μ = 464
Ha: μ ≥ 464
F.
G. H0 : μ < 464
Ha: μ ≥ 464
H. H0 : μ ≥ 464
Ha: μ > 464
I.
≠
=
<
≤
H0 : μ ≥ 464
Ha: μ ≤ 464
H0 : μ > 464
Ha: μ ≥ 464
≥
>
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Homework 7 Chapter 7-YoonJee Choi
4. Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha .
p > 0.45
Find the complement of the claim.
p (1)
0.45
Which is H0 and which is Ha?
A. H0 : p > 0.45
B. H0 : p > 0.45
C. H0 : p ≤ 0.45
Ha : p ≤ 0.45
Ha : p ≥ 0.45
Ha : p > 0.45
D. H0 : p > 0.45
Ha : p ≠ 0.45
E. H0 : p > 0.45
Ha : p > 0.45
F.
G. H0 : p < 0.45
Ha : p > 0.45
H. H0 : p > 0.45
Ha : p < 0.45
I.
(1)
<
H0 : p ≥ 0.45
Ha : p > 0.45
H0 : p ≠ 0.45
Ha : p > 0.45
≤
>
≥
≠
5. A null and alternative hypothesis are given. Determine whether the hypothesis test is lefttailed, righttailed, or
twotailed.
H0 :
p = 0.7
Ha :
p ≠ 0.7
What type of test is being conducted in this problem?
A. Lefttailed test
B. Righttailed test
C. Twotailed test
6. A null and alternative hypothesis are given. Determine whether the hypothesis test is lefttailed, righttailed, or
twotailed.
H0 :
σ
= 5
Ha :
σ
≠ 5
What type of test is being conducted in this problem?
A. Lefttailed test
B. Twotailed test
C. Righttailed test
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Homework 7 Chapter 7-YoonJee Choi
7. Find the Pvalue for a lefttailed hypothesis test with a test statistic of z = − 1.08. Decide whether to reject H0 if the level
of significance is α = 0.05.
Pvalue =
(Round to four decimal places as needed.)
State your conclusion. Choose the correct answer below.
Since P > α, reject H0 .
Since P ≤ α, reject H0 .
Since P ≤ α, fail to reject H0 .
Since P > α, fail to reject H0 .
8. Find the Pvalue for the indicated hypothesis test with the given standardized test statistic, z. Decide whether to reject
H0 for the given level of significance α.
Righttailed test with test statistic z = 1.14 and α = 0.05
Pvalue =
(Round to four decimal places as needed.)
State your conclusion.
Fail to reject H0
Reject H0
9. Find the Pvalue for the indicated hypothesis test with the given standardized test statistic, z. Decide whether to reject
H0 for the given level of significance α.
Twotailed test with test statistic z = − 2.23 and α = 0.04
Pvalue =
(Round to four decimal places as needed.)
State your conclusion.
Reject H0
Fail to reject H0
10. Find the critical value(s) for a lefttailed ztest with α = 0.07. Include a graph with your answer.
The critical value(s) is(are)
.
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
Draw a graph of the rejection region. Choose the correct graph below.
A.
B.
C.
D.
α
1
2
1
α
2
α
α
α
z
3
0
3
z
3
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0
3
z
3
0
3
z
3
0
3
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Homework 7 Chapter 7-YoonJee Choi
11. Find the critical value(s) and rejection region(s) for the type of ztest with level of significance α. Include a graph with
your answer.
Righttailed test, α = 0.04
The critical value(s) is/are z =
.
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(Round to two decimal places as needed.)
A. The rejection region is z >
.
B. The rejection region is z <
.
C. The rejection regions are z <
and z >
.
Choose the correct graph of the rejection region below.
A.
B.
0
z
C.
−z
0
D.
z
0
z
−z
0
z
12. Find the critical value(s) and rejection region(s) for the type of ztest with level of significance α. Include a graph with
your answer.
Twotailed test, α = 0.07
The critical value(s) is/are z =
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(Round to two decimal places as needed.)
A. The rejection regions are z <
and z >
B. The rejection region is z <
.
C. The rejection region is z >
.
.
Choose the correct graph of the rejection region below.
A.
B.
−z
0
z
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C.
z
0
D.
−z
0
z
0
z
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Homework 7 Chapter 7-YoonJee Choi
13. State whether the standardized test statistic z indicates that
you should reject the null hypothesis.
(a) z = 2.544
(b) z = 2.636
(c) z = − 2.381
(d) z = − 2.675
z
4 − z0 = − 2.575
0
z0 = 2.575 4
(a) For z = 2.544, should you reject or fail to reject the null hypothesis?
A. Fail to reject H0 because − 2.575 < z < 2.575.
B. Reject H0 because z > 2.575.
C. Reject H0 because − 2.575 < z < 2.575.
D. Fail to reject H0 because z > 2.575.
(b) For z = 2.636, should you reject or fail to reject the null hypothesis?
A. Fail to reject H0 because z > 2.575.
B. Reject H0 because − 2.575 < z < 2.575.
C. Fail to reject H0 because − 2.575 < z < 2.575.
D. Reject H0 because z > 2.575.
(c) For z = − 2.381, should you reject or fail to reject the null hypothesis?
A. Fail to reject H0 because z < − 2.575.
B. Reject H0 because z < − 2.575.
C. Reject H0 because − 2.575 < z < 2.575.
D. Fail to reject H0 because − 2.575 < z < 2.575.
(d) For z = − 2.675, should you reject or fail to reject the null hypothesis?
A. Reject H0 because − 2.575 < z < 2.575.
B. Reject H0 because z < − 2.575.
C. Fail to reject H0 because z < − 2.575.
D. Fail to reject H0 because − 2.575 < z < 2.575.
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14. Test the claim about the population mean, μ, at the given level of significance using the given sample statistics.
Claim: μ = 50; α = 0.07; σ = 3.46. Sample statistics: x = 49.7, n = 69
Identify the null and alternative hypotheses. Choose the correct answer below.
A. H0 : μ < 50
Ha : μ = 50
B. H0 : μ = 50
Ha : μ > 50
C. H0 : μ > 50
Ha : μ = 50
D. H0 : μ = 50
Ha : μ ≠ 50
E. H0 : μ ≠ 50
Ha : μ = 50
F. H0 : μ = 50
Ha : μ < 50
Calculate the standardized test statistic.
The standardized test statistic is
(Round to two decimal places as needed.)
.
Determine the critical value(s). Select the correct choice below and fill in the answer box to complete your choice.
(Round to two decimal places as needed.)
A. The critical value is
B. The critical values are ±
.
.
Determine the outcome and conclusion of the test. Choose the correct answer below.
A. Fail to reject H0 . At the 7% significance level, there is not enough evidence to support the claim.
B. Fail to reject H0 . At the 7% significance level, there is not enough evidence to reject the claim.
C. Reject H0 . At the 7% significance level, there is enough evidence to reject the claim.
D. Reject H0 . At the 7% significance level, there is enough evidence to support the claim.
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15. Use technology to help you test the claim about the population mean, μ, at the given level of significance, α, using the
given sample statistics. Assume the population is normally distributed.
Claim: μ ≤ 1240; α = 0.09; σ = 197.94. Sample statistics: x = 1259.62, n = 300
Identify the null and alternative hypotheses. Choose the correct answer below.
A. H0 : μ > 1259.62
Ha : μ ≤ 1259.62
B. H0 : μ > 1240
Ha : μ ≤ 1240
C. H0 : μ ≤ 1240
Ha : μ > 1240
D. H0 : μ ≥ 1240
Ha : μ < 1240
E. H0 : μ ≥ 1259.62
F. H0 : μ ≤ 1259.62
Ha : μ < 1259.62
Ha : μ > 1259.62
Calculate the standardized test statistic.
The standardized test statistic is
(Round to two decimal places as needed.)
.
Determine the Pvalue.
P=
(Round to three decimal places as needed.)
Determine the outcome and conclusion of the test.
(1)
H0 . At the 9% significance level, there (2)
(3)
the claim.
(1)
Fail to reject
(2)
Reject
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is not
is
(3)
enough evidence to
support
reject
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16. A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 769 hours. A random
sample of 30 light bulbs has a mean life of 759 hours. Assume the population is normally distributed and the
population standard deviation is 56 hours. At α = 0.08, do you have enough evidence to reject the manufacturer's
claim? Complete parts (a) through (e).
(a) Identify the null hypothesis and alternative hypothesis.
A. H0 : μ > 769
Ha : μ ≤ 769 (claim)
B. H0 : μ ≤ 759
Ha : μ > 759 (claim)
C. H0 : μ ≠ 769(claim)
Ha : μ = 769
D. H0 : μ < 759 (claim)
E. H0 : μ ≥ 769 (claim)
F. H0 : μ = 759
Ha : μ ≥ 759
Ha : μ < 769
Ha : μ ≠ 759 (claim)
(b) Identify the critical value(s). Use technology.
z0 =
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
Identify the rejection region(s). Choose the correct answer below.
A.
B.
Fail to reject H0 .
Reject H0 .
C.
Fail to reject H0 .
Reject H0 .
Fail to reject H0 .
Reject H0 .
Reject H0 .
z
4
0
4
z
4
0
4
z
4
0
4
(c) Identify the standardized test statistic. Use technology.
z=
(Round to two decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the
original claim.
A. Reject H0 . There is sufficient evidence to
reject the claim that mean bulb life is at
least 769 hours.
C. Fail to reject H0 . There is sufficient
evidence to reject the claim that mean bulb
life is at least 769 hours.
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B. Fail to reject H0 . There is not sufficient
evidence to reject the claim that mean bulb
life is at least 769 hours.
D. Reject H0 . There is not sufficient evidence
to reject the claim that mean bulb life is at
least 769 hours.
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17. A scientist estimates that the mean nitrogen dioxide level in a city is greater than
29 parts per billion. To test this estimate, you determine the nitrogen dioxide
43 26 22 36 31 36 20 35 44 34 37
levels for 31 randomly selected days. The results (in parts per billion) are listed 19 17 17 25 42 24 27 32 42 42 23
to the right. Assume that the population standard deviation is 11. At
28 41 14 18 37 21 41 28 35
α = 0.06, can you support the scientist's estimate? Complete parts (a) through
(e).
(a) Write the claim mathematically and identify H0 and Ha . Choose from the following.
A. H0 : μ = 29 (claim)
Ha : μ > 29
B. H0 : μ ≤ 29 (claim)
Ha : μ > 29
C. H0 : μ < 29
Ha : μ ≥ 29 (claim)
D. H0 : μ ≤ 29
Ha : μ > 29 (claim)
E. H0 : μ ≥ 29 (claim)
Ha : μ < 29
F. H0 : μ = 29
Ha : μ > 29 (claim)
(b) Find the critical value and identify the rejection region.
z0 =
(Round to two decimal places as needed.)
Rejection region: z (1)
(c) Find the standardized test statistic.
z=
(Round to two decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis.
Fail to reject H0
Reject H0
(e) Interpret the decision in the context of the original claim.
At the 6% significance level, there (2)
enough evidence to (3)
that the mean nitrogen dioxide level in the city is greater than 29 parts per billion.
(1)
>
<
(2)
is not
is
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(3)
the scientist's claim
support
reject
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18. Find the critical value(s) and rejection region(s) for the indicated ttest, level of significance α, and sample size n.
Lefttailed test, α = 0.005, n = 17
1
Click the icon to view the tdistribution table.
The critical value(s) is/are
.
(Round to the nearest thousandth as needed. Use a comma to separate answers as needed.)
Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice.
(Round to the nearest thousandth as needed.)
A. t <
C.
and t >
1: t-Distribution Table
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19. Find the critical value(s) and rejection region(s) for the indicated ttest, level of significance α, and sample size n.
Twotailed test, α = 0.02, n = 14
2
Click the icon to view the tdistribution table.
The critical value(s) is/are
.
(Round to the nearest thousandth as needed. Use a comma to separate answers as needed.)
Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice.
(Round to the nearest thousandth as needed.)
A. t <
C. t <
B.
and t >
2: t-Distribution Table
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20. State whether the standardized test statistic t
indicates that you should reject the null hypothesis.
Explain.
(a) t = 1.537
(b) t = 0
(c) t = − 1.403
(d) t = − 1.525
t
4
0
4
t0 = − 1.489
(a) For t = 1.537, should you reject or fail to reject the null hypothesis?
A. Fail to reject H0 , because t > − 1.489.
B. Reject H0 , because t > − 1.489.
C. Fail to reject H0 , because t < − 1.489.
D. Reject H0 , because t < − 1.489.
(b) For t = 0, should you reject or fail to reject the null hypothesis?
A. Fail to reject H0 , because t < − 1.489.
B. Reject H0 , because t > − 1.489.
C. Fail to reject H0 , because t > − 1.489.
D. Reject H0 , because t < − 1.489.
(c) For t = − 1.403, should you reject or fail to reject the null hypothesis?
A. Fail to reject H0 , because t < − 1.489.
B. Reject H0 , because t < − 1.489.
C. Reject H0 , because t > − 1.489.
D. Fail to reject H0 , because t > − 1.489.
(d) For t = − 1.525, should you reject or fail to reject the null hypothesis?
A. Reject H0 , because t > − 1.489.
B. Fail to reject H0 , because t > − 1.489.
C. Fail to reject H0 , because t < − 1.489.
D. Reject H0 , because t < − 1.489.
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21. State whether the standardized test statistic t indicates that you should reject the
null hypothesis. Explain.
(a) t = − 1.744
(b) t = 1.619
(c) t = 1.765
(d) t = − 1.741
t
4
0
− t0 = − 1.672
4
t0 = 1.672
(a) For t = − 1.744, should you reject or fail to reject the null hypothesis?
A. Reject H0 , because − 1.672 < t < 1.672.
B. Fail to reject H0 , because t > 1.672.
C. Fail to reject H0 , because t < − 1.672.
D. Reject H0 , because t < − 1.672.
(b) For t = 1.619, should you reject or fail to reject the null hypothesis?
A. Reject H0 , because t < − 1.672.
B. Fail to reject H0 , because − 1.672 < t < 1.672.
C. Fail to reject H0 , because t > 1.672.
D. Reject H0 , because − 1.672 < t < 1.672.
(c) For t = 1.765, should you reject or fail to reject the null hypothesis?
A. Fail to reject H0 , because t > 1.672.
B. Reject H0 , because − 1.672 < t < 1.672.
C. Reject H0 , because t > 1.672.
D. Fail to reject H0 , because t < − 1.672.
(d) For t = − 1.741, should you reject or fail to reject the null hypothesis?
A. Reject H0 , because − 1.672 < t < 1.672.
B. Fail to reject H0 , because t < − 1.672.
C. Reject H0 , because t < − 1.672.
D. Fail to reject H0 , because t > 1.672.
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22. Use a ttest to test the claim about the population mean μ at the given level of significance α using the given sample
statistics. Assume the population is normally distributed.
Claim: μ = 52,400; α = 0.01
3
Sample statistics: x = 52,167, s = 1800, n = 17
Click the icon to view the tdistribution table.
What are the null and alternative hypotheses? Choose the correct answer below.
A. H0: μ ≥ 52,400
Ha: μ < 52,400
B. H0: μ = 52,400
Ha: μ ≠ 52,400
C. H0: μ ≠ 52,400
Ha: μ = 52,400
D. H0: μ ≤ 52,400
Ha: μ > 52,400
What is the value of the standardized test statistic?
The standardized test statistic is
. (Round to two decimal places as needed.)
What is(are) the critical value(s)?
The critical value(s) is(are)
.
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
Decide whether to reject or fail to reject the null hypothesis.
A. Reject H0 . There is not enough evidence to reject the claim.
B. Fail to reject H0 . There is enough evidence to reject the claim.
C. Fail to reject H0 . There is not enough evidence to reject the claim.
D. Reject H0 . There is enough evidence to reject the claim.
3: t-Distribution Table
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Homework 7 Chapter 7-YoonJee Choi
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23. An employment information service claims the mean annual salary for
senior level product engineers is $97,000. The annual salaries (in
dollars) for a random sample of 16 senior level product engineers are
shown in the table to the right. At α = 0.05, test the claim that the
mean salary is $97,000. Complete parts (a) through (e) below.
Assume the population is normally distributed.
Annual Salaries
96,237 93,507
74,165 76,995
76,217 103,919
82,061 85,076
100,618
82,475
102,436
91,074
112,793
80,961
103,997
110,406
(a) Identify the claim and state H0 and Ha .
H0 :
(1)
(2)
Ha :
(3)
(4)
(Type integers or decimals. Do not round.)
The claim is the (5)
hypothesis.
(b) Use technology to find the critical value(s) and identify the rejection region(s).
The critical value(s) is/are t0 =
.
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
Choose the graph which shows the rejection region.
A.
B.
t < − t0 , t > t0
C.
t > t0
− t0 < t < t0
t
4
− t0 0 t0
D.
t < t0
t
4
4
0 t0
t
4
4
− t0 0 t0
t
4
4
t0 0
4
(c) Find the standardized test statistic, t.
The standardized test statistic is t =
.
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis.
(6)
H0 because the standardized test statistic (7)
in the rejection region.
(e) Interpret the decision in the context of the original claim.
There (8)
enough evidence at the
% level of significance to (9)
claim that the mean annual salary for senior level product engineers is (10)
integers or decimals. Do not round.)
(1)
=
≥
>
≤
p
≠
σ
(6)
(2)
μ
σ
2
(3)
(7)
Reject
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>
≥
p
<
≠
μ
≤
σ
<
Fail to reject
σ
is not
is
(4)
(8)
$
2
(5)
the
. (Type
alternative
null
=
is not
is
(9)
reject
support
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(10)
Homework 7 Chapter 7-YoonJee Choi
not equal to
equal to
greater than or equal to
less than or equal to
less than
greater than
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