Download Ch. 9 Review

Review for Chapter 9
1. For which of the following can you use a normal approximation?
a) n = 100, p = .02
b) n = 60, p = .4
c) n = 20, p = .6
d) n = 15, p = 2/3
e) n = 10, p = .7
2. What is the probability of a sample of 10 students getting an average score of 510 or more on a standardized test
if the test scores are normally distributed with a mean of 505 and a standard deviation of 50?
a) .6241
b) .4601
c) .3745
d) .1587
e) No way to determine this
3. Samples of size 49 are drawn from a distribution that's highly skewed to the right with a mean of 70 and a
standard deviation of 14. What is the probability of getting a sample mean between 71 and 73?
a) 0
b) .00023
c) .0563
d) .2417
e) No way to determine this
4. Which of the following statements are true?
I.
The larger the sample the larger the spread in the sampling distribution
II.
Provided that the population size is significantly greater than the sample size, the spread of a sampling
distribution is about the same no matter what the population size
III.
Bias has to do with the center, not the spread of a sampling distribution.
a) I and II
b) I and III
c) II and III
d) I, II, and III
e) None of the above statements are true
5.
Which of the following statements are true
I.
The sampling distribution of p (hat) has a mean equal to the population proportion p.
II.
The sampling distribution of p (hat) has a standard deviation equal to np(1  p)
III.
The sampling distribution of p (hat) is considered close to normal provided that n  30
a) I and II
b) I and III
c) II and III
d) I, II, and III
e) None of the above
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6. Which of the following are true?
I. A sampling distribution of a statistic consists of all possible random samples of the same size from a given
population
II. Regardless of the shape of the original population, for samples of size 2,  x   and  x 

n
III. Unless there was extreme skewness or outliers, we can assume that a sampling distribution of a sample mean was
approximately normal for samples of size 40.
a) I only
b) II only
c) III only
d) I and III only
e) I, II and III
7. Which answer shows:
1. The mean of the distribution x
2. The standard deviation of the distribution of x
3. The mean of the distribution of p (hat)
4. The standard deviation of the distribution of p (hat)

 p(hat) = x
 p(hat) =
p(1  p)
n
 p(hat) = p
 p(hat) =
p(1  p)
n
p(1  p)
n
 p(hat) = p
 p(hat) =
p(1  p)
n
 p(hat) = np
 p(hat) = np(1  p)
a)  x = p
x 
b)  x = 
x 
c)  x = 
x =
d)  x = np
x =
e)  x = np
 x = np(1  p)
n

n
 p(hat) =
np(1  p)  p(hat) =

n
p(1  p)
n
8. Which of the following statements are true
I.
Sample parameters are used to make inferences about populations statistics.
II.
Statistics from smaller samples have more variability.
III.
Parameters are fixed, while statistics vary depending on which sample is chosen.
a) I and II
b) I and III
c) II and III
d) I, II, and III
e) None of the above statements are true.
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9. Which of the following statements are true
I. The sampling distribution of x has a 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) I and II
b) I and III
c) II and III
d) I, II, and III
e) None of the above statements are true.
10. Which of the following statements are true
I. The mean of the set of sample means varies inversely as the square root of the size of the samples.
II. The variance of the set of sample means varies directly as the size of the samples and inversely as the variance of
the original population.
III. The standard deviation of the set of sample means varies directly as the standard deviation of the original
population and inversely as the square root of the size of the samples.
a) I only
b) II only
c) III only
d) I and II
e) I and III
11. Which of the following statements are unbiased estimators for the corresponding population parameters
I. Sample means
II. Sample proportions
III. Sample standard deviation
IV. Sample size
a) None are unbiased
b) I and II
c) I and III
d) III and IV
e) All are unbiased
12. Suppose that 35% of all business executives are willing to switch companies if offered a higher salary. If a
headhunter randomly contacts an SRS of 100 executives, what is the probability that over 40% will be willing to
switch companies if offered a higher salary?
a) .1469
b) .1977
c) .4207
d) .8023
e) .8531
13. Given that 58% of all gold dealers believe next year will be a good one to speculate in South African gold coins,
in a SRS of 150 dealers, what is the probability that between 55% and 60% believe that it will be a good year to
speculate?
a) .0500
b) .1192
c) .3099
d) .4619
e) .9215
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14. The average outstanding bill for delinquent customer accounts for a national department store chain is $187.50
with a standard deviation of $54.50. In a SRS of 50 delinquent accounts, what is the probability that the mean
outstanding bill is over $200?
a) .0526
b) .0667
c) .4090
d) .5910
e) .9474
15. The average number of daily emergency room admissions at a hospital is 85 with a standard deviations of 37. In
a SRS of 30 days, what is the probability that the mean number of daily emergency admissions is between 75 and
95?
a) .1388
b) .2128
c) .8612
d) .8990
e) .9970
16. True or False: A sampling distribution of the mean retirement age in North America can consist of as few as 100
sample values.
17. Consider drawing samples of size 2 from {A, B, C, D, E} and computing the mean of each sample. The sampling
distribution would consist of how many values?
a) 10
b) 5
c) 3
d) 100
e) 20
18. Samples of size 10 are drawn from a large (N > 10,000), symmetric population with a mean of 45 and a standard
deviation of 9. What are the mean and standard deviation of the sampling distribution of the mean for samples of
size 10, and what’s the shape of the distribution?
a) mean = 45, std. dev. = 2.95. The sample size is small, so the shape will be skewed
b) mean = 45, std. dev. = 2.95. The sample size is small, so the shape will resemble the parent population (symmetric
about its mean)
c) mean = 45, std. dev. = 2.85. The sample size is small, so the shape will resemble the parent population (symmetric
about its mean)
d) mean = 45, std. dev. = 2.85. The sample size is small, so the shape will be skewed
e) mean = 45, std. dev. = 2.85. The sample size is large, so the shape will resemble the parent population (symmetric
about its mean)
19. A population has proportion .35 of some characteristic of interest. What are the mean and standard deviation of
the sampling distribution of p-hat for samples of size 50? What’s the shape of the sampling distribution of p-hat?
a) mean = .25, std. dev. = .023. The shape appears as a uniform denisty curve.
b) mean = .35, std. dev. = .067. Not enough information to determine shape.
c) mean = .25, std. dev. = .023. The shape is skewed right.
d) mean = .35, std. dev. = .067. The shape is skewed left.
e) mean = .35, std. dev. = .067. Samples of n=50 are relatively large, so the shape is approximately normal.
20. True or False: The Central Limit Theorem tells us that the sampling distribution of a sample mean will be
approximately normal regardless of the shape of the parent population.
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21. We create a sampling distribution of x-bar by taking samples of size 70 from a population whose mean is known
to be 5 and whose standard deviation is 1. What can we say about the sampling distribution of x-bar?
a) We need information on the parent population to determine an answer.
b) The Central Limit Theorem does not apply.
c) Because n is large, the Central Limit Theorem applies
d) You can say that the shape of the sampling distribution of x-bar will be approximately normal even though you
have no info on the shape of the parent population.
e) Both c and d
22. True of False: (Refer to the previous exercise) The mean of x-bar is 5 and the standard deviation of x-bar is .12;
the last two facts would be true regardless of the shape of the original distribution or the sample size.
23. A popular soda comes in 12-oz cans. However, the actual volume of soda in the can varies normally with a mean
of 11.9 oz and a standard deviation of .3 oz. What’s the probability that the mean amount of soda in a six-pack is less
than 12 oz?
a) .082
b) .207
c) .793
d) .652
e) .792
24. Refer to #24: What’s the probability that the mean amount of soda in a six-pack is between 11.7 oz and 12 oz?
a) .096
b) .258
c) .793
d) .752
e) .742
25. The probability of winning at roulette is about .474. Suppose you bet 50 times. What’s your probability of being
even or ahead after 50 bets?
a) .36
b) .64
c) .78
d) .52
e) .42
26. Refer to #26: What’s your probability of being even or ahead after 1,000 bets?
a) .09
b) .95
c) .05
d) .75
e) .72
27. Which of the following are true?
I. A sampling distribution of a statistic consists of all possible random samples of the same size from a given
population.
II. Regardless of the shape of the original population, for samples of size 2,  X   and  X 

n
III. Unless there was extreme skewness or outliers, we can assume that a sampling distribution of a sample mean was
approximately normal for samples of size 40.
a) I only
b) II only
c) III only
d) I and III only
e) I, II, and III
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ANSWER KEY
1. B
2. C
3. D
4. C
5. E
6. E
7. B
8. C
9. D
10. C
11. B
12. A
13. D
14. A
15. C
16. FALSE
17. A
18. C
19. E
20. FALSE
21. E
22. TRUE
23. C
24. E
25. A
26. C
27. E
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