Download Name: AP Stats - Mrs. McDonald

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C.9 Review
AP Stats
1.
Following a dramatic drop of 500 points in the Dow Jones Industrial Average in September 1998, a poll conducted for the
Associated Press found that 92% of those polled said that a year from now their family financial situation will be as good
as it is today or better. The number 92% is a
(a) Statistic
(b) Sample
(c) Parameter
(d) Population
(e) None of the above. The answer is
.
2.
In a large population, 46% of the households own VCR’s. A simple random sample of 100 households is to be contacted
and the sample proportion computed. The mean of the sampling distribution of the sample proportion is
(a) 46
(b) 0.46
(c) About 0.46, but not exactly 0.46
(d) 0.00248
(e) The answer cannot be computed from the information given
3.
If a population has a standard deviation
this population is
(a) 
(b) 100 
(c)  /10
(d)  /100
(e) 0.1
4.
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. The answer is
.
5.
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. The answer is
.
 , then the standard deviation of the mean of 100 randomly selected items from
6. A simple random sample of 1000 Americans found that 61% were satisfied with the service provided by the dealer
from which they bought their car. A simple random sample of 1000 Canadians found that 58% were satisfied with the
service provided by the dealer from which they bought their car. The sampling variability associated with these
statistics is
(a) Exactly the same.
(b) Smaller for the sample of Canadians because the population of Canada is smaller than that of the United States,
hence the sample is a larger proportion of the population.
(c) Smaller for the sample of Canadians because the percentage satisfied was smaller than that for the Americans.
(d) Larger for the Canadians because Canadian citizens are more widely dispersed throughout the country than in
the United States, hence they have more variable views.
(e) About the same.
Chapter 9
1
Review AC
1. In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. Forty percent
of these show some signs of damage. Which of the following statements is correct?
(a)
(b)
(c)
(d)
(e)
40% is a parameter
40% is a statistic
40% of all trees in the forest show some signs of damage
More than 40% of the trees in the forest show some signs of damage
Less than 40% of the trees in the forest show some signs of damage
2. Refer to the previous problem. Which of the following statements is correct?
(a) The sampling distribution of the proportion of damaged trees is approximately normal
(b) If we took another random sample of trees, we would find that 40% of these would show some signs of damage
(c) If a sample of 1000 trees was examined, the variability of the sample proportion would be larger than in a sample
of 100 trees
(d) This is a comparative experiment
(e) None of the above
3. Which of the following statements is (are) true?
n even if the population is not normally distributed.
I. The sampling distribution of x has standard deviation 
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.
4. 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
5. If a statistic used to estimate a parameter is such that the mean of its sampling distribution is different from 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. The answer is
.
6. A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the mean amount
poured into the bottles is 16.05 ounces with a standard deviation of 0.1 ounce. If four bottles are randomly selected
each hour and the number of ounces in each bottle is measured, then 95% of the observations should occur in which
interval?
(a) 16.05 and 16.15 ounces
(b) –.30 and +.30 ounces
(c) 15.95 and 16.15 ounces
(d) 15.90 and 16.20 ounces
(e) None of the above
Chapter 9
2
Review AC
7. Dr. Stats plans to toss a fair coin 10,000 times in the hope that it will lead him to a deeper understanding of the laws of
probability. Which of the following statements is true?
(a) It is unlikely that Dr. Stats will get more than 5000 heads.
(b) Whenever Dr. Stats gets a string of 15 tails in a row, it becomes more likely that the next toss will be a head.
(c) The fraction of tosses resulting in heads should be close to 1/2.
(d) The chance that the 100th toss will be a head depends somewhat on the results of the first 99 tosses.
(e) All of the above statements are true.
Part 2: Free Response
Communicate your thinking clearly and completely.
7.
Suppose that you and your lab partner flip a coin 20 times and you calculate the proportion of tails to be 0.8. Your
partner seems surprised at these results and suspects that the coin is not fair. Write a brief statement that describes why
you either agree or disagree with him. Your response should relate to the principles in Chapter 9 of our text.
8.
This problem extends the previous problem. You flip the coin 20 more times and calculate the proportion of heads. You
repeat the process again and again until you have calculated 25 proportions p̂ . Your lab partner then plots a histogram
of the results on his TI-83 and overlays a boxplot for the same data as shown.
Your lab partner appears totally bewildered now. Interpret these results for
him.
A survey asks a random sample of 1500 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 p denote the proportion in the sample that says they support the increase.
Suppose that 40% of all adults in Ohio support the increase.
9.
If p̂ is the proportion of the sample who support the increase, what is the mean of p̂ ?
10.What is the standard deviation of p̂ ?
11. Explain why you can use the formula for the standard deviation of p̂ in this setting.
12. Check that you can use the normal approximation for the distribution of p̂ .
13. Find the probability that p̂ takes a value between 0.37 and 0.43.
14. How large a sample would be needed to guarantee that the standard deviation of p̂ is no more than 0.01? Explain.
Chapter 9
3
Review AC
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.
15. Compute the probability that a random sample of 50 cans produces a sample mean fill of 11.9 ounces or less. (A sketch
of the distribution is required.)
16. Suppose that each of the 25 students in a statistics class collects a random sample of 50 cans and calculates the mean
number of ounces of soda. Describe the approximate shape of the distribution for these 25 values of x .
17. What important principle that we studied is used to answer the previous question?
18. Use the 68–95–99.7 rule to find the interval that contains the middle 95% of the values of x in the sampling distribution
of x .
19. Can you calculate the probability that a single randomly selected can contains 11.9 ounces or less? If so, do it. If not,
explain why you cannot.
In a test for ESP (extrasensory perception), the experimenter looks at cards that are hidden from the subject. Each card
contains either a star, a circle, a wave, or a square. As the experimenter looks at each of 20 cards in turn, the subject
names the shape on the card.
10. Describe the design of a simulation to estimate the proportion of correct guesses assuming the subject does not have
ESP using the partial random digits table below. Then perform the simulation.
3 5 4 7 6
6 0 9 4 0
5 5 9 7 2
7 2 0 2 4
3 9 4 2 1
1 7 8 6 8
6 5 8 5 0
2 4 9 4 3
0 4 2 6 6
6 1 7 9 0
3 5 4 3 5
9 0 6 5 6
When the ESP study described above discovers a subject whose performance appears to be better than guessing, the
study continues at greater length. The experimenter looks at many cards bearing one of five shapes (star, square, circle,
wave, and cross) in an order determined by random numbers. The subject cannot see the experimenter as he looks at
each card in turn, in order to avoid any possible nonverbal clues. The answers of a subject who does not have ESP

should be independent observations, each with probability 1/5 of success. We record 1000 attempts.
11. What are the mean and standard deviation of the proportion of successes among the 1000 attempts?
12. What is the probability that a subject without ESP will be successful in at least 24% of the 1000 attempts?

13. The researcher considers evidence of ESP to be a proportion of successes so large that there is only probability 0.01
that a subject could do this well or better by guessing. What proportion of successes must a subject have to meet this
standard?
Chapter 9
4
Review AC