Chapter 18 Practice Test
Name__________________________
Part I: Multiple Choice (Questions 1-10) - Circle the answer of your choice.
1.
A news magazine claims that 30% of all New York City police officers are overweight.
Indignant at this claim, the New York City police commissioner conducts a survey in which a
random sample of 200 New York City police officers are weighed. Fifty-two, or 26%, of the
surveyed officers turn out to be overweight. Which of the following statements about this
situation is false?
(A)
(B)
(C)
(D)
(E)
The number “26%” is a parameter.
The number “30%” is a parameter.
The number “26%” is a statistic.
None of (A), (B), or (C).
All of (A), (B), or (C).
A; both B and C are true.
2.
A simple random sample of 1000 Americans found that 61% were satisfied with the service
provided by the dealer from which they bought their car. A simple random sample of 1000
Canadians found that 58% were satisfied with the satisfied with the service provided by the
dealer from which they bought their car. The sampling variability associated with these statistics
is:
(A)
(B)
about the same
much smaller for the Canadians since the population of Canada is smaller than that of the United
States, hence the sample is a larger proportion of the population.
much larger for the Canadians since Canada has a lower population density than the United
States, hence Canadians tend to live further apart which always increases sampling variability.
exactly the same
unable to be determined.
(C)
(D)
(E)
A; even though the population of the U.S. is larger than the population of Canada, the sample size is
the same and the estimated population parameters are very similar.
3.
If a statistic used to estimate a parameter is such that the mean of its sampling distribution is
equal to the true value of the parameter being estimated, the statistic is said to be:
(A)
(B)
(C)
(D)
(E)
random
biased
a proportion
unbiased
precise
D; by definition.
4.
As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local
supermarket. The probability that a shopper will buy a packet of crackers after tasting the free
sample is 0.200. Different shoppers can be regarded as independent trials. Let p̂ be the
proportion of the next shoppers that buy a packet of the crackers after tasting a free sample. How
large should n be so that the standard deviation of p̂ is no more than 0.1?
(A)
(B)
(C)
(D)
(E)
2
4
16
64
256
C;
.2 .8 
n
 .1 
.16
 .01  .01n  .16
n
5.
A factory produces plate glass with a mean thickness of 4 mm and a standard deviation of 1.1
mm. A simple random sample of 100 sheets of glass is to be measured, and the mean thickness of
the 100 sheets is to be computed. What is the probability that the average thickness of the 100
sheets is less than 4.1 mm?
(A)
(B)
(C)
(D)
(E)
0.819
0.318
0.181
0.682
0.500
1.1 

A; N  4,
 , P  x  4.1
100 

6.
The central limit theorem says that when a simple random sample of size n, where n is
sufficiently large, is drawn from any population with mean  and standard deviation  , which
of the following is true?
(A)
The standard deviation of the sample means is
(B)
(C)
(D)
(E)

.
n
The distribution of the population is exactly normal.
The distribution of the sample means is approximately normal.
The mean of the sample means is  .
The distribution of the sample standard deviations is approximately normal.
C; by definition.
7.
Forty-three percent of the people in a particular county are Democrats. A sample of 200 people is
collected at random. The approximate probability that more than 100 of the people selected are
Democrats is:
(A)
(B)
(C)
(D)
(E)
0.463
0.388
0.038
0.023
0.012

.43 .57  
 , P  pˆ  .5
D; p  .43 , N  .43,

200 


8.
If the sampling distribution of x has a mean of 12 and a standard deviation of 2 and is strongly
skewed to the right, what can be said about the population from which it came from?
(A)
(B)
(C)
(D)
(E)
Approximately normal with   12 and   2 .
Skewed right with   12 and   2 .
Approximately normal with   12 and   2 .
Skewed right with   12 and   2 .
Not enough information to determine any characteristic of the population.
B; assuming that n  1 , the sample mean is an unbiased estimator of the population mean and the
sample standard deviation should be less than the population standard deviation (as a result,    x ).
9.
The duration of Alzheimer’s disease, from the onset of symptoms until death, ranges from 3 to
20 years, with a mean of 8 years and a standard deviation of 4 years. The administrator of a large
medical center randomly selects the medical records of 30 deceased Alzheimer’s patients and
records the duration of the disease of each. Find the value L such that there is a probability of
0.99 that the average duration of the 30 patients lives less than L years above the overall mean of
8 years.
(A)
(B)
(C)
(D)
(E)
0.51
0.73
1.70
2.33
2.84
4 

C; N  8,
 , P  x  L   .99  x  9.70 , 9.70  8  1.70
30 

10.
Which of the following statements are true?
I.
II.
III.
(A)
(B)
(C)
(D)
(E)
The larger the sample, the larger the spread in the sampling distribution.
For a given sample size, provided that the population size is significantly greater the
sample size, the spread of a sampling distribution is about the same no matter what
the population size.
Bias has to do with center, not the spread, of a sampling distribution.
I and II
I and III
II and III
I, II, and III
None of the results gives the complete set of responses.
C; I is false, the larger the sample, the smaller the spread of the sampling distribution. II and III are
both true.
Part II – Free Response (Questions 11-13) – Show your work and explain your results clearly.
11.
An opinion poll asks a sample of 500 adults (an SRS) whether they favor giving parents of
school-age children vouchers that can be exchanged for education at any public or private school
of their choice. Each school would be paid by the government on the basis of how many
vouchers it collected. Suppose that in fact 45% of the population favor this idea.
(a)
What is the mean of the sampling distribution of p̂ , the proportion of adults in samples of 500
who favor giving parents of school-age children these vouchers?
 pˆ  .45
(b)
Explain why you can use the formula for the standard deviation of p̂ in this setting.
500 is less than 10% of the entire population  N  10n  N  500 10 
Note: you can only use the formula below if this condition holds. For example, if you want to sample
50 from a population of 100, you should just sample the entire population (a census).
(c)
 pˆ 
(d)
What is the standard deviation of p̂ ?
.45 .55 
500
 .022
Check that you can use the normal approximation for the distribution of p̂ .
np  10
n 1  p   10
500 .45   10
500 1  .45   10
225  10
275  10
(e)
What is the probability that more than 50% of the sample is in favor? (Sketch required.)
N .45,.022
P  pˆ  .5  .012
12.
The scores of students on the ACT college entrance examination in a recent year had the normal
distribution with mean   20.4 and standard deviation   5.8 . Round your answers to the
nearest thousandth.
(a)
What is the probability that a randomly chosen student scored 24 or higher on the ACT?
N  20.4,5.8 , P  x  24  .267
(b)
What are the mean and standard deviation of the average ACT score x for an SRS of 30
students?
 x  20.4 ,  x 
(c)
5.8
 1.059
30
What is the probability that the average ACT score of an SRS of 30 students is 24 or higher?
N  20.4,1.059 , P  x  24  .001
(d)
Would your answers to (a), (b), or (c) be affected if the distribution of ACT scores in the
population was distinctly non-normal? (Address each case.)
For (a) , the probability would not be valid because the normal distribution does not apply.
For (b) and (c), since n is large, the CLT ensures the sampling distribution will be normal. The
sampling distribution will have the given mean and standard deviation.
13.
Consider the sampling distribution of a sample mean obtained by random sampling from an
infinite population. This population has a distribution that is highly skewed toward the larger
values.
(a)
How is the mean of the sampling distribution related to the mean of the population?
They should be the same.
(b)
How is the standard deviation of the sampling distribution related to the standard deviation of the
population?
The standard deviation of the sampling distribution is the standard deviation of the population divided
by the square root of the sample size.
(c)
How is the shape of the sampling distribution affected by the sample size?
As the sample size increases the sampling distribution will become more mound-shaped and symmetric
(approximately normal).
13.
Voter registration records show that 68% of all voters in Snellville are registered as Republicans.
To test whether the numbers dialed by a random digit dialing device are really random, you use
the device to call 150 randomly chosen residential telephones in Snellville. Of the registered
voters contacted, 73% are registered Republicans.
(a)
Which percentage is a parameter and which is a statistic? Give the appropriate notation for each.
p  .68 is a parameter; pˆ  .73 is a statistic
(b)
What are the mean and standard deviation of the sample proportion of registered Republicans in
samples of size 150 from Snellville?
 pˆ  p  .68 ;  pˆ 
.68 1  .68 
150
 .038
(c)
Find the probability of obtaining an SRS of size 150 from the population of Snellville voters in
which 73% or more are registered Republicans. How well is your random digit device working?
P  pˆ  .73  .095 ; There is about a 10% chance of getting sample proportion of .73 or greater, if the
population proportion is .68. Thus, the random digit device appears to be working fine.