Chapter 9 Review Name________________________ 1. What of ...

Chapter 9 Review
Name________________________
1. What of the following best describes a sampling distribution of a statistic?
a. It is the probability that the sample statistic equals the parameter of
interest.
b. It is the probability distribution of all the values that are contained in all
possible samples of the same size.
c. It is the distribution of all of the statistics calculated from all possible
samples of the same size.
d. It is the histogram of sample statistics from all possible samples of the
same size.
e. It is none of these.
2. A simple random sample of 50 adults was asked to reveal their gross annual
incomes. The variance of this sample:
a. is always smaller than the variance of the population.
b. cannot be computed since the population size is not given.
c. equals the variance of the population.
d. is an estimate of the variance in the sampling distribution of the means of
the gross annual incomes of all possible samples.
e. is an estimate of the variance of the population but may differ from the
variance of the population.
3. A simple random sample of 100 high school seniors in a certain suburb reveals
that 65% of them have at least part-time jobs in addition to school. If the
expected value of this proportion is equal to the proportion of high school seniors
who have at least part-time jobs for the entire suburb, then we say that the sample
proportion is:
a. A true value
b. An unbiased estimator of the population proportion.
c. Equal to the population proportion
d. An estimate of whose variance equals the variance of data in the
population
e. Less than the population proportion since only 100 students were sampled.
Use the following information for questions 4 and 5. Suppose you roll a die 10 times and
record the proportion of sixes. Suppose you then conduct a simulation of this
experiment, first 100 times, then 1,000 times, and draw one histogram of the proportion
of sixes found after 100 simulations and a second histogram of the proportions of sixes
found after 1,000 simulations.
4. Which of the following is true regarding the mean of the proportions of sixes from
each simulation?
a. The mean of the proportion of sixes for the 100 simulations will be more
than the mean of the proportion of sixes for the 1,000 simulations.
b. The mean of the proportion of sixes for the 1,000 simulations will be a
better estimator of the theoretical probability of rolling a six than the mean
of the proportion of sixes for the 100 simulations.

A.P. Statistics
Mr. Johnson
c. The mean of the proportion of sixes for the 100 simulations will be less
than the mean of the proportion of sixes for the 1,000 simulations.
d. The mean of the proportion of sixes for both simulations will not estimate
the theoretical probability of rolling a six since they are finite samples
from an infinite population.
e. None of these is true.
5. Which of the following statements are true regarding the histograms of the results
form the two simulations?
I. The histograms from both simulations will be skewed left
since a fair die does not exist in nature.
II.
The histograms from both simulations will be mound-shaped
and symmetric.
III. The histogram from the experiment that has 1,000
simulations will tend to be more mound-shaped and
symmetric than the histogram from the experiment that has
100 simulations.
a. I only
b. I and II
c. II and III
d. III only
e. None of these statements is true.
6. Two simple random samples of 50 undergraduates each from two universities are
taken to determine the proportion of students who approve of the food service at
their respective schools. The first university has an enrollment of 5,000
undergraduates while the second university has an enrollment of 35,000
undergraduates. Which of the following is the most accurate statement regarding
these samples?
a. The variability of the sample from the larger university will be greater
than the variability of the sample from the smaller university.
b. The proportion of students who approve of the food service will be the
same since the sample sizes are the same.
c. The enrollment figures from the two universities are not relevant to
whether the sample statistics obtained are unbiased estimates of the
parameters of the two populations.
d. If a university with 100,000 undergraduates conducted a simple random
sample of 50 of its students, the results would be less accurate than either
sample referenced above.
e. None of these is an accurate statement.
7. Which of the following is true regarding the variation of a sampling distribution
of a sample proportion?
a. Variation depends on population size as well as sample size.
b. The variance of a sampling distribution of a sample proportion for all
samples of size 1 is 0.
Chapter 9 2 Review

A.P. Statistics
Mr. Johnson
c. As the size of the sample increases, the variation of the sampling
distribution approaches the variation of the population.
d. For a given sample size, the maximum variation in the sampling
distribution of a population proportion occurs when the sample proportion
is 0.5.
e. None of these is true.
8. The conditions that np > 10 and n(1 – p) > 10 are tested for a sampling
distribution to check for
a. A sample that is not representative of the population.
b. Bias in the response of the sample participants.
c. Skewness in the distribution.
d. A very small population size.
e. The conditions are designed to check for any of these conditions.
9. Records at a large university indicated that 20% of all freshmen are placed on
academic probation at the end of the first semester. A random sample of 100 of
this year’s freshmen indicated that 25% of them were placed on academic
probation at the end of the first semester. The results of this sample:
a. Are surprising since it indicates that 5% more of these freshmen were
placed on academic probation than was expected.
b. Are surprising since SAT scores have been increasing over the past few
years.
c. Are not surprising since the standard deviation of the sampling distribution
is 4%.
d. Are surprising since the standard deviation of the sampling distribution is
.4%.
e. Are biased since the increase of 5% could not happen without injecting
bias into the sample.
10. An investigator anticipates that the proportion of red blossoms in his hybrid plants
is .15. A random sample of 50 of his plants indicated that 22% of the blossoms
were red. Assuming that the proportion of red blossoms is .15, the standard
deviation of the sampling distribution of the sample proportion is approximately:
a. .051
b. .059
c. .07
d. .116
e. Cannot be determined
11. A sample of size 49 is drawn from a normal population with mean of 63 and
standard deviation of 14. What are the mean and standard deviation of the
distribution of sample means?
a. μ = 9, σ = 2
b. μ = 63, σ = .268
c. μ = 63, σ = 2
Chapter 9 3 Review

A.P. Statistics
Mr. Johnson
d. μ = 1.286, σ = 3.5
e. μ = 9, σ = 14
12. A sample of size 24 is drawn from a normal population with mean of 62. If the
standard deviation of the sample means is 3.5, what is the standard deviation of
the original population?
a. .056
b. .408
c. 2.48
d. 17.5
e. 87.5
13. The distribution of SAT Math scores of students taking Calculus I at a large
university is skewed left with mean 624 and standard deviation 44.5. If random
samples of 100 students are repeatedly taken, which statement best describes the
sampling distribution of sample means?
a. Normal with mean 625 and standard deviation 44.5.
b. Normal with mean 625 and standard deviation 4.45.
c. Shape unknown with mean 625 and standard deviation 44.5.
d. Shape unknown with mean 625 and standard deviation 4.45.
e. No conclusions can be drawn since the population is not normally
distributed.
14. Which of the following statements regarding the sampling distribution of sample
means is incorrect?
a. The sampling distribution is approximately normal when the population is
normal or the sample size is sufficiently large.
b. The mean of the sampling distribution is the mean of the population.
c. The standard deviation of the sampling distribution is the standard
deviation of the population.
d. The sampling distribution is found by taking repeated samples of the same
size from the population of interest and computing the mean of each
sample.
e. All of these are correct.
15. After repeated observations, it has been determined that the waiting time at the
drive-through window at a local bank on Friday afternoons between 12:00 and
6:00 PM is skewed left with a mean of 3.5 minutes and a standard deviation of 1.9
minutes. A sample of 100 customers is to be taken next Friday. What is the
probability that the mean of the sample will exceed 4 minutes?
a. .0042
b. .0369
c. .042
d. .396
e. The probability cannot be determined using a normal curve
approximation.
Chapter 9 4 Review

A.P. Statistics
Mr. Johnson
1. Suppose that 47% of all adult women think they do not get enough time to
themselves. An opinion poll interviews 1025 randomly selected women and
records the sample proportion that do not think they get enough time to
themselves.
a. Describe the sampling distribution of pˆ .
b. The truth about the population is that p = 0.47. In what range will the
middle 95% of all sample results fall?
c. What is the probability that the poll gets a sample in which fewer than
45% of women say they don’t get enough time to themselves?
Chapter 9 5 Review

A.P. Statistics
Mr. Johnson
2. The Wechsler Adult Intelligence Scale (WAIS) is a common “IQ” test for adults.
The distribution of WAIS scores for persons over 16 is approximately Normal
with mean 100 and standard deviation 15.
a. What is the probability that a randomly chosen individual has a score over
105?
b. What is the probability that the average IQ from an SRS of 60 adults is
105 or higher?
c. Would your answers be different if the distribution of WAIS scores was
distinctly nonnormal? Explain why or why not.
Chapter 9 6 Review