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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.
1) The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to
maintain a true mean temperature, µ, of 47°F, ideal for a certain type of German pilsner. The owner
of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the
true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been
conducted and that the conclusion is to reject the null hypothesis, state the conclusion in
nontechnical terms.
A) There is not sufficient evidence to support the claim that the mean temperature is different
from 47°F.
B) There is sufficient evidence to support the claim that the mean temperature is different from
47°F.
C) There is not sufficient evidence to support the claim that the mean temperature is equal to
47°F.
D) There is sufficient evidence to support the claim that the mean temperature is equal to 47°F.
Solve the problem.
2) In a hypothesis test, which of the following will cause a decrease in , the probability of making a
type II error?
A:
B:
C:
D:
Increasing while keeping the sample size n, fixed
Increasing the sample size n, while keeping fixed
Decreasing while keeping the sample size n, fixed
Decreasing the sample size n, while keeping fixed
A) A and B
B) B and C
C) A and D
2)
D) C and D
Find the P-value for the indicated hypothesis test.
3) Find the P-value for a test of the claim that less than 50% of the people following a particular diet
will experience increased energy. Of 100 randomly selected subjects who followed the diet, 47
noticed an increase in their energy level.
A) 0.5486
B) 0.2257
C) 0.2743
D) 0.7257
Solve the problem.
4) True or False: In a hypothesis test, an increase in
provided the sample size is kept fixed.
A) True
1)
will cause a decrease in the power of the test
3)
4)
B) False
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null
hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
5) With H1 : p > 0.554, the test statistic is z = 1.34.
5)
A) 0.9099; fail to reject the null hypothesis
C) 0.0901; reject the null hypothesis
B) 0.1802; reject the null hypothesis
D) 0.0901; fail to reject the null hypothesis
1
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.
6) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.
Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject
the null hypothesis, state the conclusion in nontechnical terms.
A) There is sufficient evidence to warrant rejection of the claim that the mean weight is less than
14 oz.
B) There is not sufficient evidence to warrant rejection of the claim that the mean weight is less
than 14 oz.
C) There is sufficient evidence to warrant rejection of the claim that the mean weight is at least
14 oz.
D) There is not sufficient evidence to warrant rejection of the claim that the mean weight is at
least 14 oz.
Find the P-value for the indicated hypothesis test.
7) A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of
97 such fax machines, 5% are defective. Find the P-value for a test of the manufacturer's claim.
A) 0.3409
B) 0.1736
C) 0.3264
D) 0.1591
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.
8) A psychologist claims that more than 21 percent of the population suffers from professional
problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted
and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical
terms.
A) There is not sufficient evidence to support the claim that the true proportion is greater than 21
percent.
B) There is not sufficient evidence to support the claim that the true proportion is less than 21
percent.
C) There is sufficient evidence to support the claim that the true proportion is less than 21
percent.
D) There is sufficient evidence to support the claim that the true proportion is greater than 21
percent.
6)
7)
8)
Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (µ, p, ) for the
indicated parameter.
9) Carter Motor Company claims that its new sedan, the Libra, will average better than 23 miles per
9)
gallon in the city. Use µ, the true average mileage of the Libra.
A) H0 : µ > 23
B) H0 : µ = 23
C) H0 : µ < 23
D) H0 : µ = 23
H1 : µ 23
H1 : µ > 23
H1 : µ 23
H1 : µ < 23
10) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.
A) H0 : µ < 14
B) H0 : µ = 14
C) H0 : µ > 14
D) H0 : µ = 14
H1 : µ 14
H1 : µ > 14
H1 : µ 14
2
H1 : µ < 14
10)
Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.
11) A psychologist claims that more than 2.4% of adults suffer from extreme shyness. Identify the type
11)
II error for the test.
A) Reject the claim that the percentage of adults who suffer from extreme shyness is equal to
2.4% when that percentage is actually 2.4%.
B) Reject the claim that the percentage of adults who suffer from extreme shyness is equal to
2.4% when that percentage is actually greater than 2.4%.
C) Fail to reject the claim that the percentage of adults who suffer from extreme shyness is equal
to 2.4% when that percentage is actually less than 2.4%.
D) Fail to reject the claim that the percentage of adults who suffer from extreme shyness is equal
to 2.4% when that percentage is actually greater than 2.4%.
Provide an appropriate response.
12) Suppose that you wish to test a claim about a population mean. Which distribution should be used
given that the sample is a voluntary response sample, is unknown, n = 15, and the population is
normally distributed?
A) Neither the normal nor the t-distribution
B) t-distribution
C) Normal distribution
12)
Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z
value used to test a null hypothesis.
13) = 0.09 for a right-tailed test.
13)
A) ±1.96
B) 1.34
C) 1.96
D) ±1.34
Solve the problem.
14) For large numbers of degrees of freedom, the critical 2 values can be approximated as follows:
2 = 1 (z +
2
14)
2k - 1 )2 ,
where k is the number of degrees of freedom and z is the critical value. To find the lower critical
value, the negative z-value is used, to find the upper critical value, the positive z-value is used.
Use this approximation to estimate the critical value of 2 in a right-tailed hypothesis test with
n = 143 and = 0.01.
A) 2 184.549
B) 2
C) 2
189.286
188.134
D) 2
183.411
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null
hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
15) The test statistic in a left-tailed test is z = -2.05.
15)
A) 0.4798; fail to reject the null hypothesis
B) 0.0202; reject the null hypothesis
C) 0.0404; reject the null hypothesis
D) 0.0453 fail to reject the null hypothesis
Find the critical value or values of 2 based on the given information.
16) H0 : = 8.0
n = 10
= 0.01
A) 23.209
B) 21.666
C) 2.088, 21.666
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16)
D) 1.735, 23.589
Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.
17) A consumer advocacy group claims that the mean mileage for the Carter Motor Company's new
17)
sedan is less than 32 miles per gallon. Identify the type I error for the test.
A) Fail to reject the claim that the mean is equal to 32 miles per gallon when it is actually greater
than 32 miles per gallon.
B) Reject the claim that the mean is equal to 32 miles per gallon when it is actually less than 32
miles per gallon.
C) Fail to reject the claim that the mean is equal to 32 miles per gallon when it is actually less
than 32 miles per gallon.
D) Reject the claim that the mean is equal to 32 miles per gallon when it is actually 32 miles per
gallon.
Find the P-value for the indicated hypothesis test.
18) A medical school claims that more than 28% of its students plan to go into general practice. It is
found that among a random sample of 130 of the school's students, 32% of them plan to go into
general practice. Find the P-value for a test of the school's claim.
A) 0.1635
B) 0.3461
C) 0.3078
D) 0.1539
18)
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null
hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
19) With H1 : p < 2/3, the test statistic is z = -1.89.
19)
A) 0.0294; fail to reject the null hypothesis
C) 0.0294; reject the null hypothesis
B) 0.9706; fail to reject the null hypothesis
D) 0.0588; fail to reject the null hypothesis
Find the P-value for the indicated hypothesis test.
20) A nationwide study of American homeowners revealed that 65% have one or more lawn mowers.
A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in
Omaha. Find the P-value for a test of the claim that the proportion with lawn mowers in Omaha is
higher than 65%. Among 497 randomly selected homes in Omaha, 340 had one or more lawn
mowers.
A) 0.0252
B) 0.1118
C) 0.0505
D) 0.0559
20)
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null
hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
21) The test statistic in a two-tailed test is z = 1.95.
21)
A) 0.9744; fail to reject the null hypothesis
B) 0.0512; reject the null hypothesis
C) 0.0256; reject the null hypothesis
D) 0.0512; fail to reject the null hypothesis
Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z
value used to test a null hypothesis.
22) = 0.05 for a left-tailed test.
22)
A) ±1.645
B) -1.96
C) -1.645
D) ±1.96
Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (µ, p, ) for the
indicated parameter.
23) A researcher claims that 62% of voters favor gun control.
23)
A) H0 : p < 0.62
B) H0 : p 0.62
C) H0 : p 0.62
D) H0 : p = 0.62
H1 : p
0.62
H1 : p < 0.62
H1 : p = 0.62
4
H1 : p
0.62
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null
hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
24) The test statistic in a right-tailed test is z = 1.43.
24)
A) 0.0764; reject the null hypothesis
B) 0.1528; fail to reject the null hypothesis
C) 0.1528; reject the null hypothesis
D) 0.0764; fail to reject the null hypothesis
Find the critical value or values of 2 based on the given information.
25) H1 : > 3.5
n = 14
= 0.05
A) 5.892
26) H1 :
B) 23.685
C) 22.362
25)
D) 24.736
26)
> 26.1
n=9
= 0.01
A) 20.090
B) 2.088
C) 1.646
D) 21.666
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null
hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
27) The test statistic in a right-tailed test is z = 0.52.
27)
A) 0.3015; fail to reject the null hypothesis
B) 0.0195; reject the null hypothesis
C) 0.6030; fail to reject the null hypothesis
D) 0.3015; reject the null hypothesis
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.
28) The principal of a middle school claims that test scores of the seventh-graders at his school vary
less than the test scores of the seventh-graders at a neighboring school, which have variation
described by = 14.7. Assuming that a hypothesis test of the claim has been conducted and that the
conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.
A) There is not sufficient evidence to support the claim that the standard deviation is less than
14.7.
B) There is sufficient evidence to support the claim that the standard deviation is less than 14.7.
C) There is sufficient evidence to support the claim that the standard deviation is greater than
14.7.
D) There is not sufficient evidence to support the claim that the standard deviation is greater
than 14.7.
28)
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null
hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
29) With H1 : p 0.377, the test statistic is z = 3.06.
29)
A) 0.0011; fail to reject the null hypothesis
C) 0.0011; reject the null hypothesis
B) 0.0022; fail to reject the null hypothesis
D) 0.0022; reject the null hypothesis
Solve the problem.
30) A hypothesis test is performed to test the claim that a population proportion is greater than 0.7.
Find the probability of a type II error, , given that the true value of the population proportion is
0.72. The sample size is 50 and the significance level is 0.05.
A) 0.7123
B) 0.9706
C) 0.5754
D) 0.4129
5
30)
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null
hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
31) The test statistic in a left-tailed test is z = -1.83.
31)
A) 0.9664; fail to reject the null hypothesis
B) 0.0336; reject the null hypothesis
C) 0.0672; fail to reject the null hypothesis
D) 0.0672; reject the null hypothesis
^
Find the value of the test statistic z using z =
p-p
.
pq
n
32) The claim is that the proportion of accidental deaths of the elderly attributable to residential falls is
more than 0.10, and the sample statistics include n = 800 deaths of the elderly with 15% of them
attributable to residential falls.
A) 3.96
B) 4.71
C) -3.96
D) -4.71
32)
Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (µ, p, ) for the
indicated parameter.
33) A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a
33)
standard deviation different from the = 3.3 mg claimed by the manufacturer.
3.3 mg
3.3 mg
3.3 mg
A) H0 :
B) H0 :
C) H0 : = 3.3 mg
D) H0 :
H1 :
> 3.3 mg
H1 :
= 3.3 mg
H1 :
3.3 mg
H1 :
< 3.3 mg
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.
34) Carter Motor Company claims that its new sedan, the Libra, will average better than 32 miles per
gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the
conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.
A) There is not sufficient evidence to support the claim that the mean is less than 32 miles per
gallon.
B) There is sufficient evidence to support the claim that the mean is greater than 32 miles per
gallon.
C) There is sufficient evidence to support the claim that the mean is less than 32 miles per gallon.
D) There is not sufficient evidence to support the claim that the mean is greater than 32 miles per
gallon.
Find the P-value for the indicated hypothesis test.
35) In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from
asthma. Find the P-value for a test of the claim that the proportion of all children in the town who
suffer from asthma is equal to 11%.
A) -0.2843
B) 0.2843
C) 0.5686
D) 0.2157
34)
35)
Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z
value used to test a null hypothesis.
36) = 0.08; H1 is µ 3.24
36)
A) ±1.75
B) 1.41
C) 1.75
D) ±1.41
Solve the problem.
37) True or False: In a hypothesis test regarding a population mean, the probability of a type II error, ,
depends on the true value of the population mean.
A) False
B) True
6
37)
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null
hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
38) With H1 : p 3/5, the test statistic is z = 0.78.
38)
A) 0.4354; reject the null hypothesis
C) 0.2177; reject the null hypothesis
B) 0.4354; fail to reject the null hypothesis
D) 0.2177 fail to reject the null hypothesis
Provide an appropriate response.
39) Suppose that you wish to test a claim about a population mean. Which distribution should be used
given that the sample is a simple random sample, is unknown, n = 15, and the population is not
normally distributed?
A) Normal distribution
B) Neither the normal nor the t-distribution
C) t-distribution
39)
Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.
40) A manufacturer claims that the amounts of acetaminophen in a certain brand of cold tablets have a
40)
standard deviation of 3.3 mg. Identify the type II error for the test.
A) Fail to reject the claim that the standard deviation is 3.3 mg when the standard deviation is
actually different from 3.3 mg.
B) Fail to reject the claim that the standard deviation is 3.3 mg when the standard deviation is
actually equal to 3.3 mg.
C) Reject the claim that the standard deviation is 3.3 mg when it is actually equal to 3.3 mg.
D) Reject the claim that the standard deviation is 3.3 mg when it is actually different from 3.3 mg.
Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z
value used to test a null hypothesis.
41) = 0.1 for a two-tailed test.
41)
A) ±1.645
B) ±2.33
C) ±1.4805
D) ±2.052
Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (µ, p, ) for the
indicated parameter.
42) The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to
42)
maintain a true mean temperature, µ, of 48°F, ideal for a certain type of German pilsner. The owner
of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the
true mean temperature is incorrect.
A) H0 : µ 48°
B) H0 : µ 48°
C) H0 : µ 48°
D) H0 : µ = 48°
H1 : µ > 48°
H1 : µ = 48°
H1 : µ < 48°
H1 : µ 48°
43) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO,
p, is less than 2 in every one thousand.
A) H0 : p = 0.002
B) H0 : p < 0.002
C) H0 : p = 0.002
D) H0 : p > 0.002
H1 : p > 0.002
H1 : p
0.002
H1 : p < 0.002
7
H1 : p
0.002
43)
Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.
44) A medical researcher claims that 10% of children suffer from a certain disorder. Identify the type I
44)
error for the test.
A) Reject the claim that the percentage of children who suffer from the disorder is different from
10% when that percentage really is different from 10%.
B) Fail to reject the claim that the percentage of children who suffer from the disorder is equal to
10% when that percentage is actually 10%.
C) Reject the claim that the percentage of children who suffer from the disorder is equal to 10%
when that percentage is actually 10%.
D) Fail to reject the claim that the percentage of children who suffer from the disorder is equal to
10% when that percentage is actually different from 10%.
Find the P-value for the indicated hypothesis test.
45) An article in a journal reports that 34% of American fathers take no responsibility for child care. A
researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of
225 fathers from Littleton, yielded 97 who did not help with child care. Find the P-value for a test
of the researcher's claim.
A) 0.0529
B) 0.0015
C) 0.0038
D) 0.0019
8
45)
Answer Key
Testname: TEST 3
1) B
2) A
3) C
4) B
5) D
6) C
7) A
8) A
9) B
10) D
11) D
12) A
13) B
14) D
15) B
16) D
17) D
18) D
19) C
20) D
21) D
22) C
23) D
24) D
25) C
26) A
27) A
28) B
29) D
30) B
31) B
32) B
33) C
34) B
35) C
36) A
37) B
38) B
39) B
40) A
41) A
42) D
43) C
44) C
45) D
9