SPA 3e_ Teachers Edition _ Ch 6

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C H A P T E R 6 • Sampling Distributions
Answers to Chapter 6 Practice
Test
Chapter 6
Practice Test
1. b
2. c
3. c
4. b
5. a
6. a
7. b
Section I: Multiple choice Select the best answer for each question.
1. A study of voting chose 663 registered voters at random
shortly after an election. Of these, 72% said they
had voted in the election. Election records show that
only 56% of registered voters voted in the election.
Which of the following statements is true about these
percentages?
(a) 72% and 56% are both statistics.
(b) 72% is a statistic and 56% is a parameter.
(c) 72% is a parameter and 56% is a statistic.
(d) 72% and 56% are both parameters.
2. Vermont is particularly beautiful in early October
when the leaves begin to change color. At that time of
year, a large proportion of cars on Interstate 91 near
Brattleboro have out-of-state license plates. Suppose a
Vermont state trooper randomly selects 50 cars driving
past Exit 2 on I-91, records the state identified
on the license plate, and calculates the proportion of
cars with out-of-state plates. Which of the following
describes the sampling distribution of the sample proportion
in this context?
(a) The distribution of state for all cars in the trooper’s
sample of cars passing this exit
(b) The distribution of state for all cars passing this exit
(c) The distribution of the proportion of cars with
out-of-state plates in all possible samples of 50 cars
passing this exit
(d) The distribution of the proportion of cars with
out-of-state plates in the trooper’s sample of 50 cars
passing this exit
3. A polling organization wants to estimate the proportion
of voters who favor a new law banning smoking
in public buildings. The organization decides to
increase the size of its random sample of voters from
about 1500 people to about 4000 people right before
an election. The effect of this increase is to
(a) reduce the bias of the estimate.
(b) increase the bias of the estimate.
(c) reduce the variability of the estimate.
(d) increase the variability of the estimate.
4. A machine is designed to fill 16-ounce bottles of
shampoo. When the machine is working properly, the
amount poured into the bottles follows a normal distribution
with mean 16.05 ounces and standard deviation
0.1 ounce. Assume that the machine is working
properly. If 4 bottles are randomly selected and the
number of ounces in each bottle is measured, then
there is about a 95% chance that the sample mean
will fall in which of the following intervals?
(a) 16.00 to 16.10 ounces
(b) 15.95 to 16.15 ounces
(c) 15.90 to 16.20 ounces
(d) 15.85 to 16.25 ounces
5. The central limit theorem is important in statistics
because it allows us to use the normal distribution to
find probabilities involving the sample mean if the
(a) sample size is reasonably large for any population
shape.
(b) sample size is reasonably large and the population is
normally distributed.
(c) population size is reasonably large for any population
shape.
(d) population size is reasonably large and the population
is normally distributed.
6. At a high school, 85% of students are right-handed.
Let X 5 the number of students who are right-handed
in a random sample of 10 students from the school.
Which one of the following statements about the
mean and standard deviation of the sampling distribution
of X is true?
(a) m x 5 8.5; s x ≈ 1.129
(b) m x 5 8.5; s x ≈ 0.113
(c) m x 5 8.5; s x ≈ cannot be determined from the information
given.
(d) Neither the mean nor the standard deviation can be
determined from the information given.
7. The student newspaper at a large university asks an
SRS of 250 undergraduates, “Do you favor eliminating
the carnival from the end-of-term celebration?”
In the sample, 150 of the 250 undergraduates are
in favor. Suppose that 55% of all undergraduates
favor eliminating the carnival. If you took a very
large number of SRSs of size n 5 250 from this
population, the sampling distribution of the sample
proportion p^ would have which of the following
characteri stics?
(a) Mean 0.55, standard deviation 0.03, shape unknown
(b) Mean 0.55, standard deviation 0.03, approximately
normal
(c) Mean 0.60, standard deviation 0.03, shape unknown
(d) Mean 0.60, standard deviation 0.03, approximately
normal
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