Deck 7: Sampling Distributions

Question 1

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year.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

Answer 1

B

Question 2

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.

Answer 2

C

Question 3

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 3

biased

Question 4

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 5

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.

Question 6

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year.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 7

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.

Question 8

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 9

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year.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 10

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 11

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year.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 12

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 13

Sampling distributions describe the distribution of

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

Question 14

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.

Question 15

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 16

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 pro-golfers played the course today.Find the probability that the average score of the 36 pro-golfers exceeded 71.

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

True or False: 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 19

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 size of 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 20

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 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 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 22

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year.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 23

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 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

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 25

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed,with a mean of 3.2 pounds and a 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 26

For a sample size of 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 27

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.

Question 28

True or False: 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 29

For a sample size of 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 30

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed,with a mean of 3.2 pounds and a 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 31

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 32

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed,with a mean of 3.2 pounds and a 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 33

True or False: 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 34

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 centimeter.A random sample of 12 computer chips is taken.Above what value do 2.5% of the sample means fall?

Question 35

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 15 observations.

Question 36

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 size to 25.

Question 37

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed,with a mean of 3.2 pounds and a 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 38

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 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 39

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 40

True or False: As the sample size increases,the standard error of the mean increases.

Question 41

True or False: 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 42

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 cans is to be selected.What is the probability that the sample mean will be greater than 100 grams?

Question 43

True or False: 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 44

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

Question 45

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

Question 46

True or False: A sampling distribution is a distribution for a statistic.

Question 47

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

Question 48

True or False: 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

True or False: 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 50

+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 51

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

Question 52

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 cans is to be selected.What is the probability that the sample mean will be between 100 and 120 grams?

Question 53

True or False: 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 54

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 cans is to be selected.What is the probability that the sample mean will be less than 100 grams?

Question 55

True or False: The standard error of the mean is also known as the standard deviation of the sampling distribution of the sample mean.

Question 56

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.

Question 57

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.

Question 58

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 cans is to be selected.So,95% of all sample means will be greater than how many grams?

Question 59

True or False: 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 60

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 cans is to be selected.So,the middle 70% of all sample means will fall between what two values?

Question 61

True or False: 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 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.The mean of the sampling distribution of the sample mean is ________ minutes.

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

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 66

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 67

True or False: The sample mean is an unbiased estimate of the population mean.

Question 68

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

Question 69

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 70

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 71

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 72

True or False: 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 73

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 74

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 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

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 sample sizes of 36 will be between ________ and ________.

Question 77

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 78

True or False: 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 79

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 sample sizes of 64 will be between ________ and ________.

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.The probability that the mean of the sample is between 35.95 and 35.98 oz.is ________.