Statistics (Sections 9.1 - 11.1)

Review for Test 4 Statistics (Sections 9.1 - 11.1)
You may use the cardboard tables and formula sheet, provided that there are no marks on these
sheets. On short answer problems, only use the calculatorʹs statistical package to check. Show all
work on short answer problems.
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the requested value.
1) A researcher wishes to estimate the mean resting heart rate for long-distance runners. A random
sample of 12 long-distance runners yields the following heart rates, in beats per minute.
1)
71 62 65 60 69 72
78 79 73 65 60 63
Use the data to obtain a point estimate of the mean resting heart rate for all long distance runners.
A) 69.8 beats per minute B) 66.4 beats per minute
C) 64.8 beats per minute D) 68.1 beats per minute
2) Compute the critical value zα/2 that corresponds to a 95% level of confidence.
2)
A) 2.575 B) 1.96 C) 1.645 D) 2.33
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
3) In a sample of 10 randomly selected women, it was found that their mean height was 63.4
inches. From previous studies, it is assumed that the population standard deviation, σ, is
2.4. Assume that the height of women is normally distributed. Construct the 95%
confidence interval for the population mean.
3)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
4) In a random sample of 60 computers, the mean repair cost was $150 with a population standard
deviation of $36. Construct a 99% confidence interval for the population mean.
4)
A) ($238, $274) B) ($537, $654) C) ($138, $162) D) ($18, $54)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Determine the margin of error in estimating the population mean, μ.
5) A sample of 44 washing machines yields a mean replacement time of 9.0 years. Assuming
that σ = 2.3 years, find the margin of error in estimating μ at the 90% level of confidence.
5)
Determine the sample size needed to estimate μ for the given situation.
6) E = 4, σ = 35, (1 - α) = .90 6)
1

Solve the problem.
7) In order to set rates, an insurance company is trying to estimate the number of sick days
that full time workers at an auto repair shop take per year. A previous study indicated
that the standard deviation was 2.1 days. a) How large a sample must be selected if the
company wants to be 90% confident that the true mean differs from the sample mean by
no more than 1 day b) Repeat part (a) using a 95% confidence interval. Which level of
confidence requires a larger sample size Explain.
7)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the specified t-value.
8) For a t-curve with df = 4, find t 0.05
.
8)
A) 1.645 B) 2.353 C) 2.132 D) 4.604
Solve the problem.
9) Find the critical t-value used for a confidence interval of the mean with a confidence level of 99%
and n = 10.
9)
A) 3.250 B) 2.2821 C) 1.833 D) 2.262
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
10) Find the critical t-value that corresponds to c = 0.95 and n = 16. (Note; confidence level
written as a decimal = c. So c = 0.95 is the 95% confidence level.)
10)
Find the confidence interval specified.
11) A sociologist develops a test to measure attitudes about public transportation, and 27
randomly selected subjects are given the test. Assume that the population is normally
distributed. The mean score of the sample is 76.2 and the sample standard deviation is
21.4. Construct the 95% confidence interval for the mean score of all such subjects.
11)
12) Construct a 95% confidence interval for the population mean, μ. Assume the population
has a normal distribution. A random sample of 16 fluorescent light bulbs has a mean life of
645 hours with a standard deviation of 31 hours.
12)
Solve the problem.
13) A survey of 250 households showed 19 owned at least one gun. Find a point estimate for
p, the population proportion of households that own at least one gun.
13)
14) In a survey of 10 golfers, 2 were found to be left-handed. Is it practical to construct the
90% confidence interval for the population proportion, p Explain.
14)
15) Many people think that a national lobbyʹs successful fight against gun control legislation is
reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded
2250 who are in favor of gun control legislation. Estimate the true proportion of all
Americans who are in favor of gun control legislation using a 95% confidence interval.
15)
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16) A survey of 500 non-fatal accidents showed that 222 involved the use of a cell phone.
Construct a 99% confidence interval for the proportion of non-fatal accidents that
involved the use of a cell phone.
16)
Solve the problem.
17) A researcher wishes to estimate the number of households with two cars. How large a
sample is needed in order to be 98% confident that the sample proportion will not differ
from the true proportion by more than 5% A previous study indicates that the proportion
of households with two cars is 20%.
17)
18) A state highway patrol official wishes to estimate the number of drivers that exceed the
speed limit traveling a certain road.
a) How large a sample is needed in order to be 99% confident that the sample proportion
will not differ from the true proportion by more than 3%
b) Repeat part (a) assuming previous studies found that 65% of drivers on this road
exceeded the speed limit.
18)
19) In a random sample of 60 dog owners enrolled in obedience training, it was determined
that the mean amount of money spent per owner was $109.33 per class. Assuming the
population standard deviation of the amount spent per owner is $12, construct and
interpret a 95% confidence interval for the mean amount spent per owner for an obedience
class. Interpret this interval.
19)
Construct a 95% Z-interval or a 95% t-interval about the population mean. Assume the data come from a population that
is approximately normal with no outliers. (You can use a calculator to find the sample mean and standard deviation.)
20) Fifteen randomly selected men were asked to run on a treadmill for 6 minutes. After the 6
minutes, their pulses were measured and the following data were obtained:
20)
105 94 98 88 104
101 99 85 84 124
122 114 97 101 90
Find the confidence interval specified. Assume that the population is normally distributed.
21) A savings and loan association needs information concerning the checking account
balances of its local customers. A random sample of 14 accounts was checked and yielded
a mean balance of $664.14 and a standard deviation of $297.29. Find a 98% confidence
interval for the true mean checking account balance for local customers. Assume the
population is normally distributed.
21)
Find the indicated confidence interval.
22) A researcher wishes to estimate the proportion of adults in the city of Darby who are
vegetarian. In a random sample of 1624 adults from this city, the proportion that are
vegetarian is 0.072. Find a 90% confidence interval for the true proportion of vegetarians
in the city of Darby.
22)
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23) The dean of a major university claims that the mean time for students to earn a Masterʹs
degree is less than 5.5 years. Write the null and alternative hypotheses.
23)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Classify the conclusion of the hypothesis test as a Type I error, a Type II error, or a correct decision.
24) A health insurer has determined that the ʺreasonable and customaryʺ fee for a certain medical
procedure is $1200. They suspect that the average fee charged by one particular clinic for this
procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine
whether their suspicion is correct. The hypotheses are:
H : μ = $1200
0
H : μ > $1200
1
where μ is the mean amount charged by the clinic for this procedure.
Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that
conclusion as a Type I error, a Type II error, or a correct decision, if in fact the average fee charged
by the clinic is $1200 .
A) Type II error B) Correct decision C) Type I error
24)
25) In 2000, the average duration of long-distance telephone calls originating in one town was
9.4 minutes. Five years later, in 2005, a long-distance telephone company performs a hypothesis
test to determine whether the average duration of long-distance phone calls has changed from the
2000 mean of 9.4 minutes. The hypotheses are:
H : μ = 9.4 minutes
0
H : μ ≠ 9.4 minutes
1
where μ is the mean duration, in 2005, of long-distance telephone calls originating in the town.
Suppose that the results of the sampling lead to nonrejection of the null hypothesis. Classify that
conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean duration of
long-distance phone calls has changed from the 2000 mean of 9.4 minutes.
A) Correct decision B) Type II error C) Type I error
25)
26) The mean score for all NBA games during a particular season was less than 103 points per game. If
a hypothesis test is performed, how should you interpret a decision that fails to reject the null
hypothesis (H0: μ = 103 H1: μ < 103)
26)
A) There is sufficient evidence to reject the claim μ < 103.
B) There is not sufficient evidence to support the claim μ < 103.
C) There is sufficient evidence to support the claim μ< 103.
D) There is not sufficient evidence to reject the claim μ < 103.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
27) Find the critical value for a two-tailed test with α = 0.10. 27)
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
28) Suppose you want to test the claim that μ≠ 3.5. Given a sample size of n = 45 and a level of
significance of α = 0.10, when should you reject H0 (H0: μ = 3.5 H1: μ ≠ 3.5 Assume that
you are given the population standard deviation so that you can use z.)
A) Reject H0 if the standardized test statistic is greater than 1.96 or less than -1.96
28)
B) Reject H0 if the standardized test statistic is greater than 1.645 or less than -1.645.
C) Reject H0 if the standardized test statistic is greater than 2.575 or less than -2.575
D) Reject H0 if the standardized test statistic is greater than 2.33 or less than -2.33.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
29) Test the claim that μ > 33, given that α = 0.05 and the sample statistics are n = 50, x = 33.3,
and σ = 1.2. (H0: μ = 33 H1: μ > 33 Use the classical method.)
29)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
30) Given H0: μ = 25, H1: μ ≠ 25, and P = 0.028. Do you reject or fail to reject H0 at the 0.01 level of
significance
A) not sufficient information to decide
30)
B) reject H0
C) fail to reject H0
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Perform a hypothesis test for the population mean.
31) A manufacturer makes steel bars that are supposed to have a mean length of 50 cm. A
retailer suspects that the bars are running too long. A sample of 38 bars is taken and their
mean length is determined to be 51 cm. Using a α = 0.01 level of significance, perform a
hypothesis test to determine whether the population mean is greater than 50 cm. Assume
that the population standard deviation is 3.6 cm.
31)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
32) Find the studentized test statistic t for a sample with n = 20, x = 12.4, s = 2.0, and α = 0.05 if
H0: μ

Preliminary data analyses indicate that it is reasonable to use a t-test to carry out the specified hypothesis test. Perform
the t-test using the classical method. Assume that the population is normally distributed
34) The mean waiting time for bus number 14 during peak hours used to be 10 minutes. A
public bus company official claims that more buses are now in service and that the mean
waiting time for bus number 14 during peak hours is now less than 10 minutes. Karen
took bus number 14 during peak hours on 18 different occasions. Her mean waiting time
was 7.3 minutes with a standard deviation of 2 minutes. At the 0.01 significance level, test
the claim that the mean is less than 10 minutes.
34)
Solve the problem.
35) In 2000, 36% of adults in a certain country were morbidly obese. A health practitioner
suspects that the percent has changed since then. She obtains a random sample of 1042
adults and finds that 393 are morbidly obese. Is this sufficient evidence to support the
practitionerʹs claim at the α = 0.1 level of significance
35)
Solve the problem. Assume that the population is normally distributed.
36) A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A
retailer suspects that the mean weight is actually less than 30 g. The mean weight for a
random sample of 16 ball bearings is 29.1 g with a standard deviation of 4.4 g. At the 0.05
significance level, test the claim that the mean is less than 30 g.
36)
Perform a hypothesis test for the population mean.
37) A certain manufacturer claims that the amounts of acetaminophen their cold tablets have a
mean of 600 mg. A researcher claims that the amounts of acetaminophen in these cold
tablets have a mean different from the 600 mg claimed by the manufacturer. Test this
claim at the 0.02 level of significance. The mean acetaminophen content for a random
sample of n = 38 tablets is 604.1 mg. Assume that the population standard deviation is
4.6 mg.
37)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
38) Classify the two given samples as independent or dependent.
38)
Sample 1: The weights in pounds of 26 newborn females
Sample 2: The weights in pounds of 26 newborn males
A) dependent B) independent
39) Two samples are said to be dependent if
A) Some individuals, but not all, in one sample exert influence over who is selected for inclusion
in a second ample.
B) The individuals in one sample have no influence over the selection of the individuals in a
second sample.
C) The individuals in one sample are used to determine the individuals in a second sample.
D) Sampling for inclusion in the two samples is done with replacement.
39)
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
40) Data sets A and B are dependent. Find d.
40)
A 23 21 40 36 24
B 21 17 18 28 15
Assume that the paired data came from a population that is normally distributed.
41) Construct a 99% confidence interval for data sets A and B. Data sets A and B are
dependent.
41)
A 5.8 6.8 8.7 5.7 5.8
B 8.2 7.1 7.0 6.9 8.3
Assume that the paired data came from a population that is normally distributed.
7

Answer Key
Testname: REVIEW FOR TEST 4 STAT SUM09
1) D
2) B
3) (61.9, 64.9)
4) C
5) 0.57 years
6) 208 (Recall: Always round up for n.)
7) a) 12
b) 17; A 95% confidence interval requires a larger sample than a 90% confidence interval because more information is
needed from the population to be 95% confident.
8) C
9) A
10) 2.131
11) 67.7 to 84.7
12) (628.5, 661.5)
13) 0.076
14) It is not practical to find the confidence interval. It is necessary that np^(1 - p^) ≥ 10 to insure that the distribution of p^ be
normal. (np^(1 - p^) = 1.6)
15) .5625 ± .0154 (Note: p^ = 0.5625 and n·p·(1-p) = 984 ≥10 )
16) (0.387, 0.501)
17) 347
18) a) 1844
b) 1678
19) ($106.29, $112.37); we are 95% confident that the mean amount spent per dog owner for a single obedience class is
between $106.29 and $112.37. (Note that we can use the z -interval method because we know the population standard
deviation.)
20) (93.7, 107.1); we are 95% confident that the mean pulse rate of men after 6 minutes of exercise is between 93.7 and
107.1 beats per minute.
21) $453.56 to $874.72
22) From 0.0614 to 0.0826
23) H0: μ = 5.5, H1: μ < 5.5
24) C
25) B
26) B
27) ±1.645
28) B
29) test statistic ≈ 1.77; critical value = 1.645; reject H0
30) C
31) H : μ = 50 cm
0
H : μ > 50 cm
1
α = 0.01
Classical Method: Test statistic: z = 1.71. Critical value z = 2.33.
Since 1.71. < 2.33, do not reject H0: μ = 50 cm.
P-value Method:
The P-value is about 0.0436 > α = 0.01. Do not reject H0: μ = 50 cm.
At the 1% significance level, the data do not provide sufficient evidence to conclude that the mean length of the steel
bars is greater than 50 cm.
32) B
8

Answer Key
Testname: REVIEW FOR TEST 4 STAT SUM09
33) Test statistic: t = 1.57. Critical values: t = ±1.729. Do not reject H0. There is not sufficient evidence to conclude that the
mean is different from 132.
34) H : μ = 10 minutes. H : μ < 10 minutes.
0 1
α = 0.01
Test statistic: t = -5.73. Critical value: t = -2.567. Reject H . At the 1% level of significance, there is sufficient evidence
0
to support the claim that the mean is less than 10 minutes.
35) H0: p = 0.36, H1: p ≠ 0.36, Z = 1.14, P-value = 0.2542; do not reject H0. There is not sufficient evidence at the α = 0.1
level of significance to support the practitionerʹs claim that the percentage of adults who are morbidly obese has
change since 2000.
36) H : μ = 30 g. H : μ < 30 g.
0 1
α = 0.05
Test statistic: t = -0.82. Critical value: t = -1.753. Do not reject H . At the 5% level of significance, there is not
0
sufficient evidence to support the claim that the mean is less than 30 g. (The P-value ≈ 0.213 > α. So do not reject H0.)
37) H : μ = 600 mg
0
H : μ ≠ 600 mg
1
α = 0.02
Test statistic: z = 5.49.
Critical values: z = ± 2.33.
Since 5.49 > 2.33, reject H0.
At the 2% significance level, the data do provide sufficient evidence to conclude that the mean acetaminophen content
differs from 600 mg.
38) B
39) C
40) 9.0
41) (-4.502, 2.622)
9