9-TestOfHypothesis-Exercise-1
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Ch9 Exercise: Hypothesis Testing
1) A researcher claims that less than 62% of voters favor gun control.
State the null hypothesis
and the alternative hypothesis for a test of significance.
a.
H
0
:
p
≤ 0.62
H
a
:
p
> 0.62
b.
H
0
:
p
< 0.62
H
a
:
p
≥ 0.62
c.
H
0
:
p
> 0.62
H
a
:
p
≤ 0.62
d.
H
0
:
p
≥ 0.62
H
a
:
p
< 0.62
2) In 1990, the average math SAT score for students at one school was 510. Five years later, a
teacher wants to perform a hypothesis test to determine whether the average math SAT score of
students at the school has changed from the 1990 mean of 510.
Formulate the null and
alternative hypotheses for the study described.
a.
H
0
:
≤ 510
H
a
:
> 510
b.
H
0
:
≥510
H
a
:
< 510
c.
H
0
:
= 510
H
a
:
≠ 510
d.
H
0
:
≥ 510
H
a
:
< 510
3) A long-distance telephone company claims that the mean duration of long-distance telephone
calls originating in one town was not equal to 9.4 minutes, which is the average for the state.
Determine the null and alternative hypotheses for the test described.
a.
H
0
:
≤9.4
H
a
:
> 9.4
b.
H
0
:
≠ 9.4
H
a
:
= 9.4
c.
H
0
:
= 9.4
H
a
:
≠ 9.4
d.
H
0
:
≥ 9.4
H
a
:
< 9.4
4) The standard score for a two-tail test is 2.0. What is the
P
-value?
a.
0.9772
b.
0.0456
c.
0.0228
d.
97.72
5) The standard score for a right-tail test is 2.0. What is the
P
-value?
a.
0.9772
b.
0.0456
c.
0.0228
d.
97.72
6) The standard score for a left-tail test is 2.0. What is the
P
-value?
a.
0.9772
b.
0.0456
c.
0.0228
d.
97.72
7) H
a
:
> 19,
= 8,
n
= 100; x-bar = 23;
determine whether the alternative hypothesis is
supported
(at 5% level) and give a reason for your conclusion.
a.
H
a
is not supported;
x-bar
is less than 1 standard deviation above the claimed area
b.
H
a
is not supported;
x-bar
is more than 4 standard deviations above the claimed area
c.
H
a
is supported;
x-bar
is less than 1 standard deviation above the claimed area
d.
H
a
is supported;
x-bar
is more than 4 standard deviations above the claimed area
8) z
= –1.5 for
H
a
:
≠ claimed value; What is the
P
-value for the test?
a.
6.68
b.
93.32
c.
0.0668
d.
None of the above
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9) A two-tailed test is conducted at the 5% significance level. What is the smallest
z
-score listed
below that results in rejection of the null hypothesis?
a.
1.17
b.
1.58
c.
1.81
d.
2.89
[NOTE: 1.96 is the critical value of Z in a two-tailed 5% level test. If the Z-score of our sample mean is 1.96 or
larger, we reject the null. In this question only choice (d) is bigger than 1.96 ]
10) A two-tailed test is conducted at the 10% significance level. What is the
z
-score closest to
zero in the list that will result in rejection of the null hypothesis?
a.
1.19
b.
–1.54
c.
–1.84
d.
2.59
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