Review Ch. 9
Sampling Distributions & CLT
Name:
1. A phone-in poll conducted by a newspaper reported that 73% of the 159 people who called in
liked business tycoon Donald Trump. The unknown true percentage of American citizens
who like Donald Trump is a
(a) Statistic
(b) Sample
(c) Parameter
(d) Population
(e) None of the above.
2. In the previous problem, the mean of the sampling distribution of the sample proportion is
(a) 0.73
(b) the unknown true percentage of American citizens who like Donald Trump
(c) somewhere in between 0.73 and the unknown true percentage
(d) neither 0.73 or the unknown true percentage
(e) the answer cannot be determined from the information given
3. Suppose that the unknown true percentage of American citizens who like Donald Trump is
80%. The standard deviation of the sampling distribution of the sample proportion is
(a) 0.0317
(b) 0.0352
(c) 0.765
(d) 1.25
(e) 5.04
4. The sampling distribution of a statistic is
(a) The probability that we obtain the statistic in repeated random samples
(b) The mechanism that determines whether randomization was effective
(c) The distribution of values taken by a statistic in all possible samples of the same sample
size from the same population
(d) The extent to which the sample results differ systematically from the truth
(e) None of the above.
5. A statistic is said to be unbiased if
(a) The survey used to obtain the statistic was designed so as to avoid even the hint of racial
or sexual prejudice
(b) The mean of its sampling distribution is equal to the true value of the parameter being
estimated
(c) Both the person who calculated the statistic and the subjects whose responses make up
the statistic were truthful
(d) It is used for honest purposes only
(e) None of the above.
6. 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 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.
7. Suppose we are planning on taking an SRS from a population. If we double the sample size,
then  x will be multiplied by:
(a) 2
(b) 1 2
(c) 2
(d) 1 2
(e) 4
8. Which of the following statements is (are) true?
I. The sampling distribution of x has standard deviation  n even if the population is
not normally distributed.
II. The sampling distribution of x is normal if the population has a normal distribution.
III. When n is large, the sampling distribution of x is approximately normal even if the
population is not normally distributed.
(a)
(b)
(c)
(d)
(e)
I and II
I and III
II and III
I, II, and III
None of the above gives the correct set of responses.
9. A machine is designed to fill 12- ounce bottles of soda. When the machine is working
properly the amount poured into the bottles is normally distributed with a mean of 12 ounces
and a standard deviation of 0.15 ounces. If a dozen bottles are randomly selected from each
batch filled and the number of ounces in each bottle is measured and averaged together, then
99.7% of the observations should occur in which interval?
(a) 11.55 and 12.45 ounces
(b) 11.87 and 12.13 ounces
(c) 11.91 and 12.09 ounces
(d) 11.96 and 12.04 ounces
(e) It cannot be determined since the sample size is small
Free Response.
10. Classify each underlined number as a parameter or statistic. Give the appropriate notation
for each. The National Center for Health Statistics reports that the mean systolic blood
pressure for males 35 to 44 years of age is 128 and the standard deviation is 15. The medical
director of a large company looks at the medical records of 72 executives in this age group
and finds that the mean systolic blood pressure for these executives is 126.07.
11. Below are histograms of the values taken by three sample statistics in several hundred
samples from the same population. The true value of the population parameter is marked on
each histogram with a dot and an arrow.
a. Which statistic has the largest bias among these three? Justify your answer.
b. Which statistic has the lowest variability among these three?
c. Based on the performance of the three statistics in many samples, which is preferred as an
estimate of the parameter? Why?
12. What does CLT stand for and describe what it says.
13. The weights of newborn children in the United States vary according to the normal
distribution with mean 7.5 pounds and standard deviation 1.25 pounds. The government
classifies a newborn as having low birth weight if the weight is less than 5.5 pounds.
a. What is the probability that a baby chosen at random weighs less than 5.5 pounds at
birth?
b. You choose three babies at random and compute their mean weight, x .What is the
probability that their average birth weight is less than 5.5 pounds?
c. Would your answers to a or b be affected if the distribution of birth weights in the
population were distinctly nonnormal?
14. A certain beverage company is suspected of underfilling its cans of soft drink. The company
advertises that its cans contain, on the average, 12 ounces of soda with standard deviation
0.4 ounce and follow a normal distribution.
a) If the advertisement is true is it more likely to get a random sample of 50 cans that produce a
sample mean of 11.9 ounces or less or to get a random sample of 10 cans that produces a sample
mean of 11.9 ounces or less? Justify your answer.
b) Suppose the distribution of ounces filled was an unknown distribution. Would you be able to
calculate the probabilities in part (a)? Explain why or why not.

15. Information on a packet of seeds claims that the germination rate is 92%.
a) What is the probability that more than 95% of the 160 seeds in the packet will germinate?
b) What conditions needed to be met in order to calculate the probability in part (a)? Explain
if they were clearly met or not, or have to be assumed to be met.