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1. The distribution of values taken by a statistic in all possible samples of the same size from the same
population is
(a) The probability that the statistic is obtained
(b) The population parameter
(c) The variance of the values
(d) The sampling distribution of the statistic
(e) None of the above.
2. 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) Random
(b) Biased
(c) A proportion
(d) Unbiased
(e) None of the above.
3. A sample survey of the opinions of the engineers of a small corporation is conducted. The results of
the sample indicate that the average salary is $45,987 and 60% have advanced degrees in either
business or engineering.
a) Are the numbers given above statistics or parameters?
b) Which symbols should be used to represent those numbers?
4. The graphs of the sampling distributions, I and II, of the sample mean from the same
population for samples of two different sizes are shown below. What can you conclude
about the sample sizes of Distribution I and Distribution II?
5. The graph below displays the relative frequency distribution for X, the total number of dogs and cats
owned per household, for the households in a large suburban area. For instance, 14 percent of the
households own 2 of these pets.
a) The mean and standard deviation of X are 1.65 and 1.851, respectively. Suppose 150 households
in this area are to be selected at random and X , the mean number of dogs and cats per household,
is to be computed. Describe the sampling distribution of X , including its shape, center, and
spread.
b) How will the shape, center, and spread of the sampling distribution of
households are selected instead of 150?
X be affected if 300
c) Which will have more variability, an estimate of the mean number of dogs and cats per household
that is based on 150 households or one that is based on 300 households? Explain.
6. Trains carry bauxite ore from a mine in Canada to an aluminum processing plant in northern New
York state in hopper cars. Filling equipment is used to load ore into the hopper cars. When
functioning properly, the actual weights of ore leaded into each car by the filling equipment at the
mine are approximately normally distributed with a mean of 70 tons and a standard deviation of 0.9
ton. If the mean is greater than 70 tons, the loading mechanism is overfilling.
a) If the filling equipment is functioning properly, what is the probability that a random sample of
10 cars will have a mean ore weight of 70.7 tons or more? Show your work.
b) Based on your answer in part a), if a random sample of 10 cars had a mean weight of 70.7 tons,
would you suspect that the loading mechanism was overfilling the cars? Justify your answer.
7. A polling organization asks an SRS of 1500 first-year college students how far away their home is.
Suppose that 35% of all first-year students actually attend college within 50 miles of home.
a) Describe the sampling distribution of the proportion of first-year college students in the sample
who actually attend college within 50 miles of home, including its shape, center, and spread.
b) What is the probability that more than 37% of the students in the sample attend college within 50
miles of home?
Answers:
1. D
2. D
3. a)
4.
5.
6.
7.
60% = pˆ
The sample size of Distribution II is larger than the sample size of Distribution I.
a) shape: approximately normal because the sample size (150) is large
center: x = 1.65
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spread:  x = 0.1511
b) The shape of the sampling distribution for samples of 300 will still be approximately
normal. The center will be unchanged from the sampling distribution for samples of

 150. The spread of the sampling distribution will be smaller than that of samples of
150.
c)
An estimate based on a sample of 150 will have more variability because the sampling
distribution of samples of 150 will have a larger spread than the sampling distribution
of samples of 300. Note: it is incorrect to say that a sample of 150 will have more
variability than a sample of 300. We need to compare the sampling distributions to
answer the question.
a) 0.0069 b) yes
a) shape: approximately normal center:  pˆ = 0.35 spread:  pˆ = 0.0123
b) 0.0526
statistics
b)
$45,987 = x
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