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Geography

GGR270H1

Damian Dupuy

Fall

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172 Sampling Distributions
CHAPTER 7: SAMPLING DISTRIBUTIONS
1. Sampling distributions describe the distribution of
a) parameters.
b) statistics.
c) both parameters and statistics.
d) neither parameters nor statistics.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: statistics, sampling distribution
2. The standard error of the mean
a) is never larger than the standard deviation of the population.
b) decreases as the sample size increases.
c) measures the variability of the mean from sample to sample.
d) all of the above
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: standard error, mean
3. The Central Limit Theorem is important in statistics because
a) for a large n, it says the population is approximately normal.
b) for any population, it says the sampling distribution of the sample mean is approximately
normal, regardless of the sample size.
c) for a large n, it says the sampling distribution of the sample mean is approximately
normal, regardless of the shape of the population.
d) for any sized sample, it says the sampling distribution of the sample mean is
approximately normal.
ANSWER:
c
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: central limit theorem
4. If the expectation of a sampling distribution is located at the parameter it is estimating, then we call
that statistic
a) unbiased.
b) minimum variance.
c) biased.
d) random.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: unbiased 173 Sampling Distributions
5. For air travelers, one of the biggest complaints involves the waiting time between when the airplane
taxis away from the terminal until the flight takes off. This waiting time is known to have a
skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes.
Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean
waiting time between when the airplane taxis away from the terminal until the flight takes off for
these 100 flights.
a) Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes.
b) Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes.
c) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8
minutes.
d) Distribution is approximately normal with mean = 10 minutes and standard error = 8
minutes.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: central limit theorem
6. Which of the following statements about the sampling distribution of the sample mean is
incorrect?
a) The sampling distribution of the sample mean is approximately normal whenever the
sample size is sufficiently lan≥3 ( ). 0
b) The sampling distribution of the sample mean is generated by repeatedly taking samples of
size n and computing the sample means.
c) The mean of the sampling distribution of the sample mean is equal t.
d) The standard deviation of the sampling distribution of the sample mean is equal.to
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: sampling distribution, properties
7. Which of the following is true about the sampling distribution of the sample mean?
a) The mean of the sampling distribution is always .
σ
b) The standard deviation of the sampling distribution is alwa.s
c) The shape of the sampling distribution is always approximately normal.
d) All of the above are true.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: sampling distribution, properties Sampling Distributions 174
8. True or False: The amount of time it takes to complete an examination has a skewed-left
distribution with a mean of 65 minutes and a standard deviation of 8 minutes. If 64 students were
randomly sampled, the probability that the sample mean of the sampled students exceeds 71
minutes is approximately 0.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling distribution, central limit theorem
9. Suppose the ages of students in Statistics 101 follow a skewed-right distribution with a mean of 23
years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the
following statements about the sampling distribution of the sample mean age is incorrect?
a) The mean of the sample mean is equal to 23 years.
b) The standard deviation of the sample mean is equal to 3 years.
c) The shape of the sampling distribution is approximately normal.
d) The standard error of the sample mean is equal to 0.3 years.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: sampling distribution, central limit theorem
10. Why is the Central Limit Theorem so important to the study of sampling distributions?
a) It allows us to disregard the size of the sample selected when the population is not normal.
b) It allows us to disregard the shape of the sampling distribution when the size of the
population is large.
c) It allows us to disregard the size of the population we are sampling from.
d) It allows us to disregard the shape of the population when n is large.
ANSWER:
d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: central limit theorem
11. A sample that does not provide a good representation of the population from which it was collected
is referred to as a(n) sample.
ANSWER:
biased
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: unbiased
12. True or False: The Central Limit Theorem is considered powerful in statistics because it works for
any population distribution, provided the sample size is sufficiently large and the population mean
and standard deviation are known.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate 175 Sampling Distributions
KEYWORDS: central limit theorem
13.Suppose a sample of n = 50 items is drawn from a population of manufactured products and the
weight, X, of each item is recorded. Prior experience has shown that the weight has a probability
distribution with = 6 ounces andσ = 2.5 ounces. Which of the following is true about the
sampling distribution of the sample mean if a sample of size 15 is selected?
a) The mean of the sampling distribution is 6 ounces.
b) The standard deviation of the sampling distribution is 2.5 ounces.
c) The shape of the sample distribution is approximately normal.
d) All of the above are correct.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: sampling distribution, unbiased
14. The average score of all pro golfers for a particular course has a mean of 70 and a standard
deviation of 3.0. Suppose 36 golfers played the course today. Find the probability that the average
score of the 36 golfers exceeded 71.
ANSWER:
0.0228
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability, central limit theorem
15.The distribution of the number of loaves of bread sold per day by a large bakery over the past 5
years has a mean of 7,750 and a standard deviation of 145 loaves. Suppose a random sample of n
= 40 days has been selected. What is the approximate probability that the average number of
loaves sold in the sampled days exceeds 7,895 loaves?
ANSWER:
Approximately 0
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability, central limit theorem
16. Sales prices of baseball cards from the 1960s are known to possess a skewed-right distribution
with a mean sale price of $5.25 and a standard deviation of $2.80. Suppose a random sample of
100 cards from the 1960s is selected. Describe the sampling distribution for the sample mean sale
price of the selected cards.
a) Skewed-right with a mean of $5.25 and a standard error of $2.80.
b) Normal with a mean of $5.25 and a standard error of $0.28.
c) Skewed-right with a mean of $5.25 and a standard error of $0.28.
d) Normal with a mean of $5.25 and a standard error of $2.80.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: sampling distribution, central limit theorem Sampling Distributions 176
17. Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 million in
1994. Suppose a sample of 100 major league players was taken. Find the approximate probability
that the average salary of the 100 players exceeded$1 million.
a) approximately 0
b) 0.2357
c) 0.7357
d) approximately 1
ANSWER:
d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability, central limit theorem
18. At a computer manufacturing company, the actual size of computer chips is normally distributed
with a mean of 1 centimeter and a standard deviation of 0.1 centimeters. A random sample of 12
computer chips is taken. What is the standard error for the sample mean?
a) 0.029
b) 0.050
c) 0.091
d) 0.120
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: standard error, mean
19. At a computer manufacturing company, the actual size of computer chips is normally distributed
with a mean of 1 centimeter and a standard deviation of 0.1 centimeters. A random sample of 12
computer chips is taken. What is the probability that the sample mean will be between 0.99 and
1.01 centimeters?
ANSWER:
0.2710
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability
20. At a computer manufacturing company, the actual size of computer chips is normally distributed
with a mean of 1 centimeter and a standard deviation of 0.1 centimeters. A random sample of 12
computer chips is taken. What is the probability that the sample mean will be below 0.95
centimeters?
ANSWER:
0.0416
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability 177 Sampling Distributions
21. At a computer manufacturing company, the actual size of computer chips is normally distributed
with a mean of 1 centimeter and a standard deviation of 0.1 centimeters. A random sample of 12
computer chips is taken. Above what value do 2.5% of the sample means fall?
ANSWER:
1.057
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: sampling distribution, mean, value
22. The owner of a fish market has an assistant who has determined that the weights of catfish are
normally distributed, with mean of 3.2 pounds and a standard deviation of 0.8 pounds. If a sample
of 16 fish is taken, what would the standard error of the mean weight equal?
a) 0.003
b) 0.050
c) 0.200
d) 0.800
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: standard error, mean
23.The owner of a fish market has an assistant who has determined that the weights of catfish are
normally distributed, with mean of 3.2 pounds and a standard deviation of 0.8 pounds. If a sample
of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?
a) 18.750
b) 2.500
c) 1.875
d) 0.750
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: sampling distribution, mean
24. The owner of a fish market has an assistant who has determined that the weights of catfish are
normally distributed, with mean of 3.2 pounds and a standard deviation of 0.8 pounds. If a sample
of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or
larger?
a) 0.0001
b) 0.0013
c) 0.0228
d) 0.4987
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability Sampling Distributions 178
25. The owner of a fish market has an assistant who has determined that the weights of catfish are
normally distributed, with mean of 3.2 pounds and a standard deviation of 0.8 pounds. What
percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?
a) 84%
b) 67%
c) 29%
d) 16%
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability
26. The use of the finite population correction factor, when sampling without replacement from finite
populations, will
a) increase the standard error of the mean.
b) not affect the standard error of the mean.
c) reduce the standard error of the mean.
d) only affect the proportion, not the mean.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: finite population correction
27. For sample size 16, the sampling distribution of the mean will be approximately normally
distributed
a) regardless of the shape of the population.
b) if the shape of the population is symmetrical.
c) if the sample standard deviation is known.
d) if the sample is normally distributed.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, central limit theorem
28. The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the
mean to 15, we would
a) increase the sample size to 200.
b) increase the sample size to 400.
c) decrease the sample size to 50.
d) decrease the sample to 25.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: standard error, mean 179 Sampling Distributions
29. Which of the following is true regarding the sampling distribution of the mean for a large sample
size?
a) It has the same shape, mean, and standard deviation as the population.
b) It has a normal distribution with the same mean and standard deviation as the population.
c) It has the same shape and mean as the population, but has a smaller standard deviation.
d) It has a normal distribution with the same mean as the population but with a smaller
standard deviation.
ANSWER:
d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, central limit theorem
30. For sample sizes greater than 30, the sampling distribution of the mean will be approximately
normally distributed
a) regardless of the shape of the population.
b) only if the shape of the population is symmetrical.
c) only if the standard deviation of the samples are known.
d) only if the population is normally distributed.
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: sampling distribution, mean, central limit theorem
31. For sample size 1, the sampling distribution of the mean will be normally distributed
a) regardless of the shape of the population.
b) only if the shape of the population is symmetrical.
c) only if the population values are positive.
d) only if the population is normally distributed.
ANSWER:
d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, central limit theorem
32. The standard error of the proportion will become larger
a) as p approaches 0.
b) as p approaches 0.50.
c) as p approaches 1.00.
d) as n increases.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: standard error, proportion Sampling Distributions 180
33. True or False: As the sample size increases, the standard error of the mean increases.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: standard error, mean
34. True or False: If the population distribution is symmetric, the sampling distribution of the mean
can be approximated by the normal distribution if the samples contain at least 15 observations.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: population distribution, sampling distribution, mean, central limit theorem
35. True or False: If the population distribution is unknown, in most cases the sampling distribution of
the mean can be approximated by the normal distribution if the samples contain at least 30
observations.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: sampling distribution, mean, central limit theorem
36. True or False: If the amount of gasoline purchased per car at a large service station has a
population mean of $15 and a population standard deviation of $4, then 99.73% of all cars will
purchase between $3 and $27.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability
37. True or False: If the amount of gasoline purchased per car at a large service station has a
population mean of $15 and a population standard deviation of $4, and a random sample of 4 cars
is selected, there is approximately a 68.26% chance that the sample mean will be between $13 and
$17.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
EXPLANATION: The sample is too small for the normal approximation.
KEYWORDS: sampling distribution, mean, probability 181 Sampling Distributions
38. True or False: If the amount of gasoline purchased per car at a large service station has a
population mean of $15 and a population standard deviation of $4, and it is assumed that the
amount of gasoline purchased per car is symmetric, there is approximately a 68.26% chance that a
random sample of 16 cars will have a sample mean between $14 and $16.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability
39. True or False: If the amount of gasoline purchased per car at a large service station has a
population mean of $15 and a population standard deviation of $4, and a random sample of 64
cars is selected, there is approximately a 95.44% chance that the sample mean will be between $14
and $16.
ANSWER:
True
TYPE: TF DIFFICULTY: Difficult
KEYWORDS: sampling distribution, mean, probability
40. True or False: As the sample size increases, the effect of an extreme value on the sample mean
becomes smaller.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling distribution, law of large numbers
41. True or False: If the population distribution is skewed, in most cases the sampling distribution of
the mean can be approximated by the normal distribution if the samples contain at least 30
observations.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: sampling distribution, mean, central limit theorem
42. True or False: A sampling distribution is a probability distribution for a statistic.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling distribution Sampling Distributions 182
μ σ 2
43. True or False: Suppose = 50 and = 100 for a population. In a sample where n = 100 is
randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability
2
44. True or False: Suppose = 80 andσ = 400 for a population. In a sample where n = 100 is
randomly taken, 95% of all possible sample means will fall above 76.71.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability
μ 2
45. True or False: Suppose = 50 andσ = 100 for a population. In a sample where n = 100 is
randomly taken, 90% of all possible sample means will fall between 49 and 51.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: sampling distribution, mean, probability
46. True or False: The Central Limit Theorem ensures that the sampling distribution of the sample
mean approaches normal as the sample size increases.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: central limit theorem
47. True or False: The standard error of the mean is also known as the standard deviation of the
sampling distribution of the sample mean.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: standard error, mean
48. True or False: A sampling distribution is defined as the probability distribution of possible sample
sizes that can be observed from a given population.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: sampling distribution 183 Sampling Distributions
49. True or False: As the size of the sample is increased, the standard deviation of the sampling
distribution of the sample mean for a normally distributed population will stay the same.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: standard error, properties
50. True or False: For distributions such as the normal distribution, the arithmetic mean is considered

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