Deck 7: Sampling Distributions

Question 1

The mean of the sampling distribution of the sample mean is the mean of:

A)the means of all possible samples of the same size taken from the population
B)the frequency distribution of the population
C)the means of all frequency distributions
D)one sample

Answer 1

the means of all possible samples of the same size taken from the population

Question 2

A population contains 14 members.The total number of samples of size 8 that you can select (without replacement)from this population is:

Answer 2

3,003

Question 3

The mean weekly earnings of all employees of a company are $822.The mean weekly earnings of a random sample of 25 employees selected from this company is $837.The difference ($837 - $822 = $15)is the:

A)probability error
B)nonsampling error
C)sampling error
D)population error

Answer 3

sampling error

Question 4

A population contains 8 members.The total number of samples of size 4 that you can select (without replacement)from this population is:

Question 5

The population distribution is the probability distribution of the:

A)whole population of a country
B)population data
C)population means
D)population probabilities

Question 6

The mean age of all students at a university is 24 years.The mean age of a random sample of 100 students selected from this university is 23.6 years.The difference (23.6 - 24 = -0.4)is the:

A)probability error
B)nonsampling error
C)sampling error
D)population error

Question 7

The mean price of all magazines published in the United States is $3.65.The mean price of a random sample of 16 magazines is $4.30.The sampling error is:

Question 8

The sampling distribution is the probability distribution of a:

A)sample
B)sample with replacement
C)sample without replacement
D)sample statistic

Question 9

As the sample size increases,the standard deviation of the sampling distribution of the sample mean:

A)increases
B)decreases
C)remains the same
D)Unable to determine

Question 10

When the sample size is greater than 1,the standard deviation of the sampling distribution of the sample means is always:

A)equal to the standard deviation of the population
B)smaller than the standard deviation of the population
C)greater than the standard deviation of the population
D)none of these

Question 11

If is less than or equal to 0.05,the standard deviation of the sampling distribution of the sample mean is equal to the population standard deviation:

A)divided by the square of the sample size
B)divided by the sample size
C)divided by the square root of the sample size
D)multiplied by the sample size

Question 12

The sampling error is:

A)an error that occurs during collection,recording,and tabulation of data
B)the difference between the value of a sample statistic and the value of the corresponding population parameter
C)an error that occurs when a sample of fewer than 30 members is drawn
D)an error that occurs when a sample of 30 or more members is drawn

Question 13

For a continuous random variable x,the population mean and the population standard deviation are 82 and 18,respectively.You take a simple random sample of 25 elements from this population.The mean of the sampling distribution of the sample mean is:

Question 14

An error that occurs because of chance is called:

A)nonsampling error
B)sampling error
C)mean error
D)probability error

Question 15

The standard deviation of the sampling distribution of the sample mean for a sample size of n drawn from a population with a mean of and a standard deviation of is:

A)
B)
C)
D)

Question 16

The mean of the sampling distribution of the sample mean is:

A)always equal to the sample mean
B)sometimes equal to the population mean
C)always equal to the population mean
D)always equal to the sampling procedure

Question 17

The probability distribution of a sample statistic is the:

A)frequency distribution of that statistic
B)binomial distribution of that statistic
C)sampling distribution of that statistic
D)Poisson distribution of that statistic

Question 18

The mean age of all cars registered in the United States is 7.50 years.The mean age of a random sample of 1,000 cars is 6.9.The sampling error is:

Question 19

For a continuous random variable x,the population mean and the population standard deviation are 139 and 9,respectively.You take a simple random sample of 36 elements from this population.The mean of the sampling distribution of the sample mean is:

Question 20

An error that occurs because of human mistakes is called:

A)nonsampling error
B)sampling error
C)mean error
D)probability error

Question 21

If the population from which samples are drawn is not normally distributed,then the sampling distribution of the sample mean is:

A)never normally distributed
B)approximately normally distributed if n is 30 or larger
C)always normally distributed
D)approximately normally distributed if n is less than 30

Question 22

The number of hours spent per week on household chores by all adults has a mean of 28.1 hours and a standard deviation of 6.0 hours.The probability,rounded to four decimal places,that the mean number of hours spent per week on household chores by a sample of 53 adults will be more than 26.75 is:

Question 23

A continuous random variable x has a right-skewed distribution with a mean of 45 and a standard deviation of 6.The sampling distribution of the sample mean for a sample of 25 elements taken from this population is:

A)approximately normal
B)normal
C)skewed to the right
D)skewed to the left

Question 24

The daily sales at a convenience store have a mean of $1280 and a standard deviation of $172.Assuming ,the standard deviation of the sampling distribution of the mean sales of a sample of 16 days for this convenience store,rounded to two decimal places,is:

Question 25

A continuous random variable x has a left-skewed distribution with a mean of 155 and a standard deviation of 28.The sampling distribution of the sample mean for a sample of 75 elements taken from this population is:

A)approximately normal
B)not normal
C)skewed to the right
D)skewed to the left

Question 26

For a continuous random variable x,the population mean and the population standard deviation are 95 and 40,respectively.Assuming ,the standard deviation of the sampling distribution of the sample mean for a sample of 49 elements taken from this population,rounded to two decimals,is:

Question 27

A continuous random variable x has a normal distribution with a mean of 90 and a standard deviation of 15.The sampling distribution of the sample mean for a sample of 16 elements taken from this population is:

A)not normal
B)normal
C)skewed to the right
D)skewed to the left

Question 28

A population has a normal distribution with a mean of 79.6 and a standard deviation of 13.3.Assuming ,the probability,rounded to four decimal places,that the sample mean of a sample of size 18 elements selected from this populations will be less than 80.1 is:

Question 29

A population has a mean of 98.2 and a standard deviation of 25.2.Assuming ,the probability,rounded to four decimal places,that the sample mean of a sample of size 89 elements selected from this population will be between 91 and 97 is:

Question 30

To apply the Central Limit Theorem to the sampling distribution of the sample mean,the required sample is typically large enough if:

A)n is greater than 50
B)n is 50 or less
C)n is less than 30
D)n is 30 or larger

Question 31

A population has a mean of 60.5 and a standard deviation of 13.5.Assuming ,the probability,rounded to four decimal places,that the sample mean of a sample of size 35 elements selected from this populations will be between 62.5 and 67.1 is:

Question 32

A continuous random variable x has a left-skewed distribution with a mean of 130 and a standard deviation of 22.The sampling distribution of the sample mean for a sample of 16 elements taken from this population is:

A)approximately normal
B)normal
C)skewed to the right
D)skewed to the left

Question 33

For a continuous random variable x,the population mean and the population standard deviation are 69 and 15,respectively.Assuming ,the standard deviation of the sampling distribution of the sample mean for a sample of 16 elements taken from this population,rounded to two decimals,is:

Question 34

The weights of all babies born at a hospital have a mean of 7.3 pounds and a standard deviation of 0.65 pounds.The mean of the sampling distribution of the mean weight of a sample of 41 babies born at this hospital is:

Question 35

The weights of all babies born at a hospital have a mean of 7.4 pounds and a standard deviation of 0.66 pounds.Assuming ,the standard deviation of the sampling distribution of the mean weight of a sample of 32 babies born at this hospital,rounded to three decimal places,is:

Question 36

According to the Central Limit Theorem,the sampling distribution of the sample mean is approximately normal,irrespective of the shape of the population distribution,if:

A)n is 30 or larger
B)n is less than 30
C)np and nq are both greater than 5
D)n is 50 or larger

Question 37

A population has a normal distribution with a mean of 51.4 and a standard deviation of 8.4.Assuming ,the probability,rounded to four decimal places,that the sample mean of a sample of size 18 elements selected from this populations will be more than 51.15 is:

Question 38

The daily sales at a convenience store have a mean of $1,297 and a standard deviation of $134.The mean of the sampling distribution of the mean sales of a sample of 17 days for this convenience store is:

Question 39

A continuous random variable x has a right-skewed distribution with a mean of 80 and a standard deviation of 12.The sampling distribution of the sample mean for a sample of 50 elements taken from this population is:

A)approximately normal
B)not normal
C)skewed to the right
D)skewed to the left

Question 40

If the population from which samples are drawn is normally distributed,then the sampling distribution of the sample mean is:

A)not normally distributed
B)normally distributed if n is 30 or larger
C)always normally distributed
D)normally distributed if n is less than 30

Question 41

Use the following to answer questions :
Forty percent of all students at a large university live on campus.Suppose you extract a sample of 115 students from this university.The sample proportion is the proportion of students in this sample who live on campus.
The standard deviation of the sampling distribution of this sample proportion,rounded to four decimal places,is:

Question 42

The standard deviation of the sampling distribution of the sample proportion is equal to:

A)the population standard deviation divided by the square root of n
B)the population standard deviation divided by n
C)the square root of
D)

Question 43

Use the following to answer questions :
Suppose that 6.5% or all persons are allergic to penicillin .A sample of 561 persons is selected.
The probability that less than 8% of persons in the sample of will be allergic to penicillin,rounded to four decimal places,is approximately:

Question 44

Suppose the proportion of elements of a population that possess a certain characteristic is 0.34.Assuming ,the probability that the sample proportion for a sample of 472 elements drawn from this population is more than .33,rounded to four decimal places,is approximately:

Question 45

In a sample of 859 adults,437 are in favor of banning all advertisements relating to alcohol.The proportion of these adults who are in favor of banning all advertisements relating to alcohol,rounded to three decimal places,is:

Question 46

The sampling distribution of the sample proportion is approximately normal if:

A)n is greater than or equal to 30
B)np and nq are both greater than 10
C)np and nq are both greater than 5
D)np and nq are both less than 5

Question 47

A company has 411 employees and 104 of them are college graduates.The proportion of employees of this company who are college graduates,rounded to three decimal places,is:

Question 48

Use the following to answer questions :
A study shows 18.0% of all adult males did not visit their physicians' offices last year.A sample of 623 adult males is selected.
The probability that more than 18% of adult males in the sample did not visit their physicians' offices last year,rounded to four decimal places,is approximately:

Question 49

Use the following to answer questions :
A study shows 18.0% of all adult males did not visit their physicians' offices last year.A sample of 623 adult males is selected.
The probability that less than 22.5% of adult males in the sample did not visit their physicians' offices last year,rounded to four decimal places,is approximately:

Question 50

The time spent commuting from home to work for all employees of a very large company has a normal distribution with a mean of 43.4 minutes and a standard deviation of 12.1 minutes.The probability,rounded to four decimal places,that the mean time spent commuting from home to work by a sample of 21 employees will be between 43.26 and 49.35 minutes is:

Question 51

A class of 61 students has 15 seniors.The proportion of students in this class who are seniors,rounded to three decimal places,is:

Question 52

Use the following to answer questions :
Thirty-five percent of all adults read at least one newspaper daily.Suppose you select a sample of 486 adults.The sample proportion is the proportion of adults in this sample who read at least one newspaper daily.
The mean of the sampling distribution of this sample proportion is:

Question 53

The mean of the sampling distribution of the sample proportion is equal to the population:

A)mean
B)mean divided by n
C)proportion
D)proportion divided by n

Question 54

Use the following to answer questions :
Suppose that 6.5% or all persons are allergic to penicillin .A sample of 561 persons is selected.
The probability that 7.5% to 9% of persons in a the sample will be allergic to penicillin,rounded to four decimal places,is approximately:

Question 55

Suppose the proportion of elements of a population that possess a certain characteristic is 0.62.Assuming ,the probability that the sample proportion for a sample of 120 elements drawn from this population is between .62 and .67,rounded to four decimal places,is approximately:

Question 56

If you divide the number of elements in a population with a specific characteristic by the total number of elements in the population,the dividend is the population:

A)mean
B)proportion
C)distribution
D)sampling distribution

Question 57

Use the following to answer questions :
Forty percent of all students at a large university live on campus.Suppose you extract a sample of 115 students from this university.The sample proportion is the proportion of students in this sample who live on campus.
The mean of the sampling distribution of this sample proportion is:

Question 58

Use the following to answer questions :
Thirty-five percent of all adults read at least one newspaper daily.Suppose you select a sample of 486 adults.The sample proportion is the proportion of adults in this sample who read at least one newspaper daily.
The standard deviation of the sampling distribution of this sample proportion,rounded to four decimal places,is:

Question 59

In the case of proportion,the sample size is large if:

A)n is greater than or equal to 30
B)np and nq are both less than 5
C)n is less than 30
D)np and nq are both greater than 5

Question 60

If you divide the number of elements in a sample with a specific characteristic by the total number of elements in the sample,the dividend is the:

A)sample mean
B)sample proportion
C)sample distribution
D)sampling distribution

Question 61

The following table shows the population probability distribution of x,the random variable representing the price per ticket,in dollars,for 20 upcoming concerts at a certain community's civic center.
How many of the 20 concerts will cost $53 per ticket?

Question 62

A company has 15,000 employees and 10,800 of them have completed a particular training course.Management decides to choose a random sample from all employees.What is the minimum number of employees that must be in the sample in order to use the Central Limit Theorem to approximate the distribution of the proportion in the sample who have taken the training course?

Question 63

There are 2,000 bicycles in a community.The owners of 1,250 of these bicycles also own locks for the bikes.A sample of 184 bicycles is chosen,and it just so happens that the proportion of bicycles in the sample that have locks is the same as that for the entire community.How many of the bicycles in the sample have locks?

Question 64

A continuous random variable x has a normal distribution with a mean of 51 and a standard deviation of 26.The sampling distribution of the sample mean for a sample of 16 elements has what mean and standard deviation?

Question 65

Suppose the number of books consulted by a student last weekend has distribution
Let X₁ and X₂ be independent and each have the same distribution as the population.
Determine the missing elements in the table for the sampling distribution of .

Question 66

For a sample from a normal distribution with standard deviation ,the standard deviation of the sampling distribution of the sample mean is /3.What is the size of the sample?

Question 67

You ask 2,500 actors in the Screen Actors Guild (SAG)if they have ever appeared in a production of Shakespeare's King Lear.1,225 of them say "yes",while the others say "no".The value p is the proportion of the actors who have appeared in King Lear.You next draw a random sample of 11 actors from the SAG.What are the mean and standard deviation of the sample proportion? Round the mean to two decimal places and the standard deviation to four decimal places.

Question 68

Suppose you are analyzing four different brands of soda.The sodium content,in milligrams,of one can of each of these brands has a distribution with a mean of 45.2 mg and a standard deviation of 8.8600 mg.You take a random sample of 2 cans from a large supply of cans including all four brands of soda.Let be the mean of this sample.What are the mean and standard deviation of the sampling distribution of ?

Question 69

A continuous random variable x has a right-skewed distribution with a mean of 72 and a standard deviation of 36.The sampling distribution of the sample mean for a sample of 100 elements has what mean and standard deviation?

Question 70

A population consists of five elements: 5,6,8,10,and 13.You choose a random sample of three elements from this population (without replacement).Which of the following is not a possible value of the sample mean?

A)6.33
B)8.00
C)9.33
D)10.67

Question 71

All 1,035 members at a country club take part in a contest to see who can drive a golf ball the farthest.Each member takes three swings,and his/her best drive is entered into the contest.The distances of the drives entered into the contest have a mean of 188.3 yards and a standard deviation of 16.2 yards.You select a sample of 43 drives,what is the probability,rounded to four decimal places,that the mean of the sample exceeds 192 yards?

Question 72

Extensive data suggest that the number of overtime hours paid by a large company per month can be modeled as distribution with mean 3.5 and standard deviation 1.4.
If P₁ is the probability that the mean of a sample of size 55 lies in the interval (2.9,4.1)and P₂ is the probability that the mean of a sample of size 110 lies in the interval (2.9,4.1),then

A)P₁ = P₂
B)P₁ > P₂
C)P₁ < P₂
D)P₁ = 2P₂

Question 73

A continuous random variable x has a left-skewed distribution with a mean of 101 and a standard deviation of 72.The sampling distribution of the sample mean for a sample of 64 elements has what mean and standard deviation?

Question 74

A continuous random variable x has a normal distribution with a mean of 65 and a standard deviation of 21.In the sampling distribution of the sample mean for a sample of 25 elements,what is the z-score for a sample mean of 68.36?

Question 75

You select 15 people at random from a population of 10,000 and ask them how many movies they have rented in the past month.Their responses are:
4 0 6 0 8 3 7 6 5 0 1 4 2 9 5
You know that the mean number of movies rented in the past month by the population is 5.0.Assuming that you made no non-sampling errors,what is the sampling error for the mean?

Question 76

The number of hot dogs sold per game at one concession stand at a baseball park is normally distributed with = 23,750 and = 106.You select 13 games at random,and the mean number of hot dogs sold, ,is denoted.What is the standard deviation of ,rounded to three decimal places?