Deck 7: Sampling Distributions

Question 1

Which of the following is true about the sampling distribution of the sample mean?

A) The mean of the sampling distribution is always μ.
B) The standard deviation of the sampling distribution is always σ.
C) The shape of the sampling distribution is always approximately normal.
D) All of the above are true.

Answer 1

A

Question 2

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 2

biased

Question 3

Suppose the ages of students in Statistics 101 follow a right skewed 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 sampling distribution is equal to 23 years.
B) The standard deviation of the sampling distribution is equal to 3 years.
C) The shape of the sampling distribution is approximately normal.
D) The standard error of the sampling distribution is equal to 0.3 years.

Answer 3

B

Question 4

If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic

A) unbiased.
B) minimum variance.
C) biased.
D) random.

Question 5

The mean score of all pro golfers for a particular course has a mean of 70 and a standard
deviation of 3.0. Suppose 36 pro golfers played the course today. Find the probability that the
mean score of the 36 pro golfers exceeded 71.

Question 6

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.

Question 7

Sales prices of baseball cards from the 1960s are known to possess a right skewed 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) Right skewed 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) Right skewed 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

Question 8

Sampling distributions describe the distribution of

A) parameters.
B) statistics.
C) both parameters and statistics.
D) neither parameters nor statistics.

Question 9

Suppose a sample of n = 50 items is selected 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 μ = 6 ounces and σ = 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 sampling distribution is approximately normal.
D) All of the above are correct.

Question 10

For air travelers, one of the biggest complaints is of 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 right
Skewed 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 right skewed with mean = 10 minutes and standard error = 0.8 minutes.
B) Distribution is right skewed 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.

Question 11

The distribution of the number of loaves of bread sold per week 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 weeks has been selected. What is the approximate probability that the mean number of
loaves sold in the sampled weeks exceeds 7,895 loaves?

Question 12

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the
Approximate probability that the mean salary of the 100 players exceeded $3.5 million.

A) Approximately 0
B) 0.0228
C) 0.9772
D) Approximately 1

Question 13

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.

Question 14

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the
Approximate probability that the mean salary of the 100 players was no more than $3.0 million.

A) Approximately 0
B) 0.0151
C) 0.9849
D) Approximately 1

Question 15

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.

Question 16

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.

Question 17

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 large (n ≥ 30 ).
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 to μ.
D) The standard deviation of the sampling distribution of the sample mean is equal to σ.

Question 18

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. What was the
Standard error for the sample mean salary?

A) $0.012 million
B) $0.12 million
C) $12 million
D) $1,200.0 million

Question 19

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the
Approximate probability that the mean salary of the 100 players exceeded $4.0 million.

A) Approximately 0
B) 0.0228
C) 0.9772
D) Approximately 1

Question 20

The amount of time it takes to complete an examination has a left skewed
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.

Question 21

The standard error of the population proportion will become larger

A) as population proportion approaches 0.
B) as population proportion approaches 0.50.
C) as population proportion approaches 1.00.
D) as the sample size increases.

Question 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 standard deviation of 0.8 pound. 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%

Question 23

At a computer manufacturing company, the actual size of a particular type of computer chips is
normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A
random sample of 12 computer chips is taken. What is the probability that the sample mean will
be below 0.95 centimeters?

Question 24

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.

Question 25

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.

Question 26

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.

Question 27

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 standard deviation of 0.8 pound. 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

Question 28

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.

Question 29

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the
Approximate probability that the mean salary of the 100 players was less than $2.5 million.

A) Approximately 0
B) 0.0151
C) 0.9849
D) Approximately 1

Question 30

If the amount of gasoline purchased per car at a large service station has a
population mean of 15 gallons and a population standard deviation of 4 gallons, then 99.73% of
all cars will purchase between 3 and 27 gallons.

Question 31

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.

Question 32

At a computer manufacturing company, the actual size of a particular type of computer chips is
normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A
random sample of 12 computer chips is taken. Above what value do 2.5% of the sample means
fall?

Question 33

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.

Question 34

At a computer manufacturing company, the actual size of a particular type of computer chips is
normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. 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?

Question 35

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 standard deviation of 0.8 pound. 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

Question 36

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 standard deviation of 0.8 pound. 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

Question 37

If the population distribution is symmetric, the sampling distribution of the mean
can be approximated by the normal distribution if the samples contain 15 observations.

Question 38

If the amount of gasoline purchased per car at a large service station has a
population mean of 15 gallons and a population standard deviation of 4 gallons 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 gallons.

Question 39

As the sample size increases, the standard error of the mean increases.

Question 40

At a computer manufacturing company, the actual size of a particular type of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. 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

Question 41

μ The am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. What is the probabilityally distributed with
that the sample mean will be between 100 and 120 grams?

Question 42

The amount of time required for an oil and filter change on an automobile is normally
distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample
of 16 cars is selected. What is the standard error of the mean?

Question 43

A sampling distribution is a distribution for a statistic.

Question 44

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. So, the mally distributed with iddle 70% of
all sample means will fall between what two values?

Question 45

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. What is the probabilityally distributed with
that the sample mean will be greater than 100 grams?

Question 46

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.

Question 47

For distributions such as the normal distribution, the arithmetic mean is
considered more stable from sample to sample than other measures of central tendency.

Question 48

Suppose μ = 80 and σ = 20 for a population. In a sample where n = 100 is
randomly taken, 95% of all possible sample means will fall above 76.71.

Question 49

The standard error of the mean is also known as the standard deviation of the
sampling distribution of the sample mean.

Question 50

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. So, 95% of all samally distributed with ple
means will be greater than how many grams?

Question 51

The Central Limit Theorem ensures that the sampling distribution of the sample
mean approaches a normal distribution as the sample size increases.

Question 52

If the amount of gasoline purchased per car at a large service station has a
population mean of 15 gallons and a population standard deviation of 4 gallons 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 gallons.

Question 53

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.

Question 54

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. What is the ally distributed with
probability that the sample mean will be less than 100 grams?

Question 55

If the amount of gasoline purchased per car at a large service station has a
population mean of 15 gallons and a population standard deviation of 4 gallons 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 gallons.

Question 56

Suppose μ = 50 and σ = 10 for a population. In a sample where n = 100 is
randomly taken, 90% of all possible sample means will fall between 49 and 51.

Question 57

Suppose μ = 50 and σ = 10 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.

Question 58

A sampling distribution is defined as the probability distribution of possible
sample sizes that can be observed from a given population.

Question 59

The fact that the sample means are less variable than the population data can be
observed from the standard error of the mean.

Question 60

As the sample size increases, the effect of an extreme value on the sample mean
becomes smaller.

Question 61

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard
deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The
probability that the mean of the sample is between 35.94 and 36.06 oz. is __________.

Question 62

The amount of time required for an oil and filter change on an automobile is normally
distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample
of 16 cars is selected. What is the probability that the sample mean will be between 39 and 48
minutes?

Question 63

A manufacturer of power tools claims that the mean amount of time required to assemble their
top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a
random sample of 64 purchasers of this table saw is taken. So, the middle 95% of the sample
means based on samples of size 64 will be between __________ and __________.

Question 64

The amount of time required for an oil and filter change on an automobile is normally
distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample
of 16 cars is selected. 90% of the sample means will be greater than what value?

Question 65

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a
standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this
machine. The sampling distribution of the sample mean has a standard error of 0.15.

Question 66

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard
deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The
probability that the mean of the sample is less than 36.03 is __________.

Question 67

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a
standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this
machine. The sampling distribution of the sample mean has a mean of 36 oz.

Question 68

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard
deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The
probability that the mean of the sample is between 35.95 and 35.98 oz. is __________.

Question 69

A manufacturer of power tools claims that the mean amount of time required to assemble their
top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a
random sample of 64 purchasers of this table saw is taken. The probability that the sample mean
will be less than 82 minutes is __________.

Question 70

A manufacturer of power tools claims that the mean amount of time required to assemble their
top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a
random sample of 64 purchasers of this table saw is taken. The standard deviation of the sampling
distribution of the sample mean is __________ minutes.

Question 71

To use the normal distribution to approximate the binomial distribution, we need ______ and
______ to be at least 5.

Question 72

The sample mean is an unbiased estimate of the population mean.

Question 73

The amount of time required for an oil and filter change on an automobile is normally
distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample
of 16 cars is selected. 95% of all sample means will fall between what two values?

Question 74

The amount of time required for an oil and filter change on an automobile is normally
distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample
of 16 cars is selected. What is the probability that the sample mean is between 45 and 52
minutes?

Question 75

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard
deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The
probability that the mean of the sample exceeds 36.01 oz. is __________.

Question 76

A manufacturer of power tools claims that the mean amount of time required to assemble their
top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a
random sample of 64 purchasers of this table saw is taken. The probability that the sample mean
will be greater than 88 minutes is __________.

Question 77

A manufacturer of power tools claims that the mean amount of time required to assemble their
top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a
random sample of 64 purchasers of this table saw is taken. The mean of the sampling distribution
of the sample mean is __________ minutes.

Question 78

A manufacturer of power tools claims that the mean amount of time required to assemble their
top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a
random sample of 64 purchasers of this table saw is taken. The probability that the sample mean
will be between 77 and 89 minutes is __________.

Question 79

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a
standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this
machine. The sampling distribution of the sample mean will be approximately normal only if the
population sampled is normal.

Question 80

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard
deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. So,
the middle 95% of the sample means based on samples of size 36 will be between __________
and __________.