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Chapter 7: Sampling Distributions
Chapter 7 Reflection
The Practice of Statistics, 4th edition – For AP*
STARNES, YATES, MOORE
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Chapter 7 Test Recap:
#1 Multiple Choice – Answer D
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1. A survey conducted by Black Flag asked whether or not the
action of a certain type of roach disk was effective in killing
roaches. 79% of the respondents agreed that the roach disk was
effective. The number 79% is a
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(A.) parameter.
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(B.) population.
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(C.) sampling distribution.
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(D.) statistic
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(E.) sample
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Chapter 7 Test Recap:
#2 Multiple Choice – Answer A
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2. Below are dot plots of the values taken by three different
statistics in 30 samples from the same population. The true value
of the population parameter is marked with an arrow. The statistic
that has the largest bias among these three is
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(A) statistic A.
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(B) statistic B.
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(C ) statistic C.
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(D) A and B have similar bias, and it is larger than the bias of C.
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(E)B and C have similar bias, and it is larger than the bias of A.
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Chapter 7 Test Recap:
#3 Multiple Choice – Answer C
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3. If we took a SRS of 1700 people from California (population 34
million) and a SRS of 1000 people from Detroit (population 1
million) which sampling distribution would have the smaller
standard deviation?
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(A.) Detroit, because 1000/1,000,000 is more than 1700/32,000,000.
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(B.) Detroit, because it has the smaller population.
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(C.) California, because the sample size (1700) is larger than for
Detroit (1000).
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(D.) California, because it has the larger population.
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(E.) Both would be the same, because simple random samples (SRS)
are taken in both places.
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Chapter 7 Test Recap:
#4 & #5 Multiple Choice –
Answers C & D
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A 2010 study of 240 randomly-selected residents of a subtropical resort city
with 82,000 residents found that 5.4% of them had been exposed to the
mosquito-borne virus that causes Dengue fever. Suppose the actual
percentage of people in the city who have been exposed to the virus is 3%. Let
p = the proportion of residents who have been exposed in a random sample of
240,
5. Which of the following conditions had to be
4. The standard deviation of p is approximately
met in order for us to use the formula for that
we used in the previous question?
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(A.) 0.000121.
(A.) n ≥ 30
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(B.) 0.00187.
(B.) np(1-p) ≥ 10
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(C.) 0.0110.
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(D.) 2.643.
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(E.) 2.683.
(C.) np ≥10 and n(1-p) ≥ 10
(D.) n < 0.10N
(E.)The population distribution is approximately
Normal.
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Chapter 7 Test Recap:
#6 Multiple Choice
Answer: 30 ≤ n ≤ 75
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6.The histogram below was obtained from data on 750 high school
basketball games in a regional athletic conference. It represents the
number of three-point baskets made in each game.
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What is the range of sample sizes the research could take from this
population without violating conditions required for the application of
the formula
and the central limit theorem?
7 Test Recap:
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#7 Multiple Choice – Answer B
7. 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 sample mean
thickness of the 100 sheets is to be computed.
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We know the random variable has approximately a normal
distribution because of the
(A.) law of large numbers.
(B.) central limit theorem.
(C.) law of proportions.
(D.) fact that probability is the long run proportion of times an event occurs.
(E.) normality of the population distribution.
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Chapter 7 Test Recap:
#8 Multiple Choice – Answer C
8. In a large population of adults, the mean IQ is 112 with a
standard deviation of 20. Suppose 200 adults are randomly
selected for a market research campaign. The sampling
distribution of the sample mean IQ is
(A.) exactly Normal, mean 112, standard deviation 20.
(B.) approximately Normal, mean 112, standard deviation 0.1.
(C.) approximately Normal, mean 112, standard deviation 1.414.
(D.) approximately Normal, mean 112, standard deviation 20.
(E.) exactly Normal, mean 112, standard deviation 1.414.
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Chapter 7 Test Recap:
#9 Multiple Choice – Answer B
9. A census of the labor force in a large metropolitan area found
that the time it takes for people to commute to work has a mean
of 20.5 minutes and a standard deviation of 15.4 minutes. Which
of the following represents the probability that a random sample
of 40 people have a mean commute time that is greater than 25
minutes?
(A.)
P ( z  1.848)
(B.)
P( z  1.848)
(C.)
P ( z  0.292)
(D.)
P( z  0.292)
(E.)
P( z  1.820)
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Chapter 7 Test Recap:
#10 Multiple Choice – Answer D
10. A survey asks a random sample of 500 adults in Ohio if they
support an increase in the state sales tax from 5% to 6%, with the
additional revenue going to education. Let denote the proportion
in the sample who say they support the increase. Suppose that
53% of all adults in Ohio support the increase. What is the
correct notation and probability that less than half the sample will
say they support the increase?
A.
P( z  0.0027)  0.4989
B.
P( z  0.0027)  0.5011
C.
P( z  1.344)  0.0895
D.
P( z  1.344)  0.0895
E.
P( z  0.134)  0.0895
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11. For each description below, identify each underlined number
as a parameter or statistic. Use
appropriate notation to describe each number, e.g., = 0.96.
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+ 12.Suppose two different statistics—call them Statistic A and
Statistic B—can be used to estimate the same population
parameter. Statistic A has lower bias than B, and A also has
low variability compared to B. On the two axes below, draw two
parallel dotplots showing 8 values of each statistic that are
consistent with these characteristics. Assume that the parameter
value is at the arrow on the axes.
Statistic A
Statistic B