Deck 6: Sampling and Sampling Distributions

Question 1

A sample of size 25 is selected at random from a finite population.If the finite population correction factor is 0.80,then the population size is:

A)121
B)96
C)75
D)100

Answer 1

121

Question 2

Random samples of size 36 are taken from an infinite population whose mean is 80 and standard deviation is 18.The standard error of the sample mean is:

A)18
B)15
C)3
D)2

Answer 2

3

Question 3

Why is the central limit theorem important in statistics?

A)Because for a large sample size n,it says the population is approximately normal.
B)Because for any population,it says the sampling distribution of the sample mean is approximately normal,regardless of the shape of the population.
C)Because for a large sample size n,it says the sampling distribution of the sample mean is approximately normal,regardless of the shape of the population.
D)Because for any sample size n,it says the sampling distribution of the sample mean is approximately normal.

Answer 3

Because for a large sample size n,it says the sampling distribution of the sample mean is approximately normal,regardless of the shape of the population.

Question 4

The standard deviation of the sampling distribution of the sample mean is also called the:

A)minimum sample factor.
B)standard error of the mean.
C)finite population correction factor.
D)population standard deviation.

Question 5

What is the name of the parameter that determines the shape of the chi-square distribution?

A)mean
B)variance
C)proportion
D)degrees of freedom

Question 6

The sampling distribution of the mean is a distribution of:

A)individual population values.
B)individual sample values.
C)sample statistics.
D)population parameters.

Question 7

A sample of size n is selected at random from an infinite population.As n increases,which of the following statements is true?

A)The population standard deviation decreases.
B)The standard error of the sample mean decreases.
C)The population standard deviation increases.
D)The standard error of the sample mean increases.

Question 8

In examining the invoices issued by a company,an auditor finds that the dollar amounts of invoices have a mean of $1,732 and a standard deviation of $298.What is the probability that for a sample of 45 invoices,the average invoice is greater than $1,800?

A)0.563
B)0.063
C)0.437
D)0.937

Question 9

Which of the following statements is true regarding the standard error of the mean?

A)It is equal to the population variance divided by the square root of n.
B)It is equal to the population standard deviation divided by the sample size n.
C)It is equal to the population variance divided by (n -1).
D)It is equal to the population standard deviation divided by the square root of n.

Question 10

If all possible samples of size n are drawn from an infinite population with a mean of 20 and a standard deviation of 5,then the standard error of the sampling distribution of sample means is equal to 1.0 only for samples of size:

A)5
B)15
C)20
D)25

Question 11

If the standard error of the sampling distribution of the sample proportion is 0.0229 for samples of size 400,then the population proportion must be either:

A)0.4 or 0.6
B)0.5 or 0.5
C)0.2 or 0.8
D)0.3 or 0.7

Question 12

In a recent survey of high school students,it was found that the average amount of money spent on entertainment each week was normally distributed with a mean of $52.30 and a standard deviation of $18.23.Assuming these values are representative of all high school students,what is the probability that for a sample of 25,the average amount spent by each student exceeds $60?

A)0.3372
B)0.0174
C)0.1628
D)0.4826

Question 13

If a sample of size 100 is taken from a population whose standard deviation is equal to 100,then the standard error of the mean is equal to:

A)10
B)100
C)1,000
D)10,000

Question 14

Which of the following distributions is used to determine the sampling distribution of the sample variance?

A)normal distribution
B)binomial distribution
C)chi-square distribution
D)Poisson distribution

Question 15

As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion only if:

A)the sample size n is greater than 30.
B)the population proportion P is close to 0.50.
C)the underlying population is normal.
D)nP(1 - P)> 5.

Question 16

If all possible samples of size n are drawn from an infinite population with a mean μ and a standard deviation σ,then the standard error of the sampling distribution of sample mean is inversely proportional to:

A)μ
B)σ
C)n
D)

Question 17

The interval within which a sample mean has a high probability of occurring,given that the population mean and variance is known,is called a(n):

A)confidence interval.
B)rejection interval.
C)acceptance interval.
D)decision interval.

Question 18

In a recent survey of college professors,it was found that the average amount of money spent on entertainment each week was normally distributed with a mean of $95.25 and a standard deviation of $27.32.What is the probability that the average spending of a sample of 25 randomly-selected professors will exceed $102.50?

A)0.0918
B)0.1064
C)0.3936
D)0.4082

Question 19

The number of students using the ATM on campus daily is normally distributed with a mean of 237.6 and a standard deviation of 26.3.For a random sample of 55 days,what is the probability that the ATM usage averaged more than 230 students per day?

A)0.9756
B)0.9483
C)0.9838
D)0.9524

Question 20

The amount of time that you have to wait before seeing the doctor in the doctor's office is normally distributed with a mean of 15.2 minutes and a standard deviation of 15.2 minutes.If you take a random sample of 35 patients,what is the probability that the average wait time is greater than 20 minutes? (Hint: Round the probability value to 2 decimal places. )

A)0.28
B)0.16
C)0.09
D)0.03

Question 21

If the sample size,n,equals the population size,N,then the variance of the sample mean,
,is zero.

Question 22

Based on the sampling distribution of the means and the central limit theorem,the sample mean can be used as a good estimator of the population mean,assuming that the sample size,n,is sufficiently large.

Question 23

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that 20% of all invoices are for amounts greater than $800.A random sample of 50 invoices is taken.
Based on the central limit theorem,the mean of all possible sample means is equal to the population:

A)variance.
B)mean.
C)median.
D)standard deviation.

Question 24

All possible random samples of 200 middle managers are selected from a population for a study concerning their mean annual income.The population standard deviation is computed to be $2,248.5.What is the standard deviation of the sampling distribution of the means?

A)$47.42
B)$11.24
C)$158.99
D)$57.86

Question 25

A basketball player shoots 60 free throws a day and historically makes 75 percent of them.What is the probability that he will make at most 80 percent tomorrow?

A)0.1056
B)0.8133
C)0.1867
D)0.8944

Question 26

Random samples of size 36 each are taken from a large population whose mean is 120 and standard deviation is 39.The standard error of the sampling distribution of sample mean is:

A)39
B)6.5
C)15.6
D)24.5

Question 27

As the size of the sample increases,what happens to the shape of the sampling distribution of sample means?

A)It becomes positively skewed.
B)It becomes negatively skewed.
C)It becomes uniformly distributed.
D)It becomes approximately normal.

Question 28

If the standard error of the sampling distribution of the sample proportion is 0.02049 for samples of size 500,then the population proportion must be either:

A)0.2 or 0.8
B)0.5 or 0.5
C)0.3 or 0.7
D)0.6 or 0.4

Question 29

A golfer practices 60 twenty-foot putts a day and historically makes 25 percent of them.Calculate the standard error of the sample proportion.

A)0.3256
B)0.6258
C)0.0559
D)0.4057

Question 30

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that 20% of all invoices are for amounts greater than $800.A random sample of 50 invoices is taken.
What is the probability that at least 25% of these 50 invoices are for more than $800?

A)0.1894
B)0.8106
C)0.3106
D)0.8894

Question 31

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
You have recently joined a Weight Watchers club.Suppose that the number of times you expect to visit the club in a month is represented by a normally distributed random variable with a mean of 12 and a standard deviation of 2.50.
The probability is 85% that you average less than how many visits to the club per month over the course of next year?

A)12.75
B)11.50
C)12.50
D)11.75

Question 32

The standard deviation of is also called the:

A)standard error of the sampling distribution of sample proportions.
B)standard deviation of the population.
C)normal approximation to the binomial.
D)continuity correction factor.

Question 33

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that 20% of all invoices are for amounts greater than $800.A random sample of 50 invoices is taken.
The average score of all students who took a particular statistics class last semester has a mean of 70 and a standard deviation of 3.0.Suppose 36 students who are taking the class this semester are selected at random.Find the probability that the average score of the 36 students exceeds 71.

A)0.0228
B)0.0772
C)0.1228
D)0.1772.

Question 34

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that 20% of all invoices are for amounts greater than $800.A random sample of 50 invoices is taken.
Suppose that 15% of all invoices are for amounts greater than $1,000.A random sample of 60 invoices is taken.What is the probability that between 13% and 23% of these 60 invoices are for more than $1,000?

A)0.4591
B)0.2019
C)0.1664
D)0.6255

Question 35

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that 20% of all invoices are for amounts greater than $800.A random sample of 50 invoices is taken.
What is the mean and standard error of the sample proportion of invoices with amounts in excess of $800?

A)mean = 10,standard error = 0.4472
B)mean = 0.20,standard error = 0.0566
C)mean = 0.20,standard error = 0.0032
D)mean = 10,standard error = 0.0598

Question 36

The variance of the sampling distribution of the sample mean is equal to the variance of the population mean divided by the square root of the sample size.

Question 37

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that 20% of all invoices are for amounts greater than $800.A random sample of 50 invoices is taken.
What is the probability that more than 22.7% of these 50 invoices are for more than $800?

A)0.1368
B)0.2266
C)0.3156
D)0.2734

Question 38

According to the central limit theorem,the sampling distribution of the sample mean can be approximated by the normal distribution as the:

A)number of samples gets large enough.
B)sample size gets large enough.
C)population standard deviation increases.
D)sample standard deviation decreases.

Question 39

If all possible random samples of size n are taken from a population,and the mean of each sample is determined,the mean of the sample distribution is:

A)larger than the population mean.
B)exactly the same as the population mean.
C)smaller than the population mean.
D)unrelated to the population mean.

Question 40

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
You have recently joined a Weight Watchers club.Suppose that the number of times you expect to visit the club in a month is represented by a normally distributed random variable with a mean of 12 and a standard deviation of 2.50.
Over the course of the next year,what is the probability that you average more than 13 visits to the club?

A)0.1554
B)0.4177
C)0.3446
D)0.0823

Question 41

The fraction of the population in the sample determines the precision of results from a random sample.

Question 42

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose you flip a coin four times.For every head,you receive one point,and for every tail,you lose one point.
What is the probability that the mean number of points you receive on four flips is 0.5?

Question 43

The chi-square family of distributions is used in applied statistical analysis because it provides a link between the sample and population variances.

Question 44

The mean of the sampling distribution of the sample proportion
,when the sample size n = 100 and the population proportion P = 0.92,is 92.0

Question 45

The central limit theorem is basic to the concept of statistical inference because it permits us to draw conclusions about the population based strictly on sample data.

Question 46

The variance of the sampling distribution of the sample proportion is equal to P(1 - P)/ n.

Question 47

The standard error of the mean is also called sampling error.

Question 48

If a random sample of 250 observations is taken from a population whose proportion P is equal to 0.6,then the expected value of the sample proportion
is 0.40

Question 49

The central limit theorem states that as the sample size increases,the distribution of the population mean approaches the normal distribution.

Question 50

Acceptance intervals are widely used for quality control monitoring of various production and service processes.

Question 51

The central limit theorem states that if all possible random samples of size n are taken from any population,the sampling distribution of sample means becomes approximately normal when the sample size n is large enough.

Question 52

The variance of the sampling distribution of sample mean
decreases as the sample size,n,increases.

Question 53

The central limit theorem states that the sampling distribution of sample means will closely resemble the normal distribution regardless of the sample size.

Question 54

The mean and variance of a chi-square distribution with ν degrees of freedom is determined by the number of degrees of freedom.

Question 55

The standard error of the sampling distribution of the sample proportion
,when the sample size n = 100 and the population proportion P = 0.30,is 0.0021

Question 56

If the standard error of the sampling distribution of sample proportions is 0.0245 for samples of size 400,then the population proportion must be 0.40.

Question 57

The sampling distribution of sample means is normal for samples of any size,n,provided that the parent sampled population has a normal distribution.

Question 58

The central limit theorem can be applied to both discrete and continuous random variables.

Question 59

The larger the sample size,the larger the standard error of the sample proportion.

Question 60

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose you flip a coin four times.For every head,you receive one point,and for every tail,you lose one point.
Develop the sampling distribution for the mean number of points you receive from flipping four coins.

Question 61

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
You have recently joined a country club.Suppose that the number of times you expect to play golf in a month is represented by a normally distributed random variable with a mean of 10 and a standard deviation of 2.4.
Over the course of the next year,what is the probability that you average more than 11 games a month?

Question 62

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable X follow a normal distribution with a mean of μ and a standard deviation of σ.Let
₁ be the mean of a sample of 16 observations randomly chosen from this population,and
₂ be the mean of a sample of 25 observations randomly chosen from the same population.
Suppose that 15% of all invoices are for amounts greater than $1,000.A random sample of 60 invoices is taken.What is the mean and standard error of the sample proportion of invoices with amounts in excess of $1,000? What is the probability that the proportion of invoices in the sample is greater than 18%?

Question 63

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
In a recent survey of high school students,it was found that the average amount of money spent on entertainment each week was normally distributed with a mean of $52.30 and a standard deviation of $18.23.Assume that these values are representative of all high school students.
The probability is 65% that the average spending of a sample of 25 randomly-selected students will spend at least how much?

Question 64

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The length of time it takes to fill an order at a local sandwich shop is normally distributed with a mean of 4.1 minutes and a standard deviation of 1.3 minutes.
The probability is 95% that the average waiting time for a random sample of ten customers is greater than how many minutes?

Question 65

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
It has been found that 62.1% of all unsolicited third class mail delivered to households goes unread.Over the course of a month,a household receives 100 pieces of unsolicited mail.
What is the probability that the sample proportion is greater than 0.60?

Question 66

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A sample of 25 bottles is taken from the production line at a local bottling plant.Assume that the fill amounts follow a normal distribution.
What is the probability that the sample standard deviation is more than 70% of the population standard deviation?

Question 67

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable X follow a normal distribution with a mean of μ and a standard deviation of σ.Let
₁ be the mean of a sample of 16 observations randomly chosen from this population,and
₂ be the mean of a sample of 25 observations randomly chosen from the same population.
Evaluate the statement P
₁ < μ +
)< P(
₂ < μ +
)as to whether it is true or false.Please state if you are unable to determine whether the statement is true or false.Support your answer.

Question 68

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
It has been found that 62.1% of all unsolicited third class mail delivered to households goes unread.Over the course of a month,a household receives 100 pieces of unsolicited mail.
What is the variance of the proportion?

Question 69

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
In a recent survey of high school students,it was found that the average amount of money spent on entertainment each week was normally distributed with a mean of $52.30 and a standard deviation of $18.23.Assume that these values are representative of all high school students.
What is the probability that for a sample of 25,the average amount spent exceeds $60?

Question 70

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A sample of 25 bottles is taken from the production line at a local bottling plant.Assume that the fill amounts follow a normal distribution.
The probability is 90% that the sample variance is less than what percent of the population variance?

Question 71

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The length of time it takes to fill an order at a local sandwich shop is normally distributed with a mean of 4.1 minutes and a standard deviation of 1.3 minutes.
What is the probability that the average waiting time for a random sample of ten customers is between 4.0 and 4.2 minutes?

Question 72

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
It has been found that 62.1% of all unsolicited third class mail delivered to households goes unread.Over the course of a month,a household receives 100 pieces of unsolicited mail.
What is the standard error of the sample proportion?

Question 73

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
It has been found that 62.1% of all unsolicited third class mail delivered to households goes unread.Over the course of a month,a household receives 100 pieces of unsolicited mail.
What is the mean of the sample proportion of pieces of unread mail?

Question 74

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The filling machine at a bottling plant is operating correctly when the variance of the fill amount is equal to 0.3 ounces.Assume that the fill amounts follow a normal distribution.
The probability is 0.10 that for a sample of 30 bottles,the sample variance is less than what number?

Question 75

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose you flip a coin four times.For every head,you receive one point,and for every tail,you lose one point.
What is the probability that the mean number of points you receive on four flips is 0?

Question 76

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable X follow a normal distribution with a mean of μ and a standard deviation of σ.Let
₁ be the mean of a sample of 16 observations randomly chosen from this population,and
₂ be the mean of a sample of 25 observations randomly chosen from the same population.
Evaluate the statement P(
₁ < μ +
)< P(
₂ < μ +
)as to whether it is true or false.Please state if you are unable to determine whether the statement is true or false.Support your answer.

Question 77

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
You have recently joined a country club.Suppose that the number of times you expect to play golf in a month is represented by a normally distributed random variable with a mean of 10 and a standard deviation of 2.4.
The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4.For a particular sample size,the probability that the sample mean exceeds 300 is 0.2.How big must the sample be?

Question 78

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
You have recently joined a country club.Suppose that the number of times you expect to play golf in a month is represented by a normally distributed random variable with a mean of 10 and a standard deviation of 2.4.
Over the course of the next year,the probability is 85% that you average less than how many games per month?

Question 79

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The filling machine at a bottling plant is operating correctly when the variance of the fill amount is equal to 0.3 ounces.Assume that the fill amounts follow a normal distribution.
What is the probability that for a sample of 30 bottles,the sample variance is greater than 0.5?

Question 80

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable X follow a normal distribution with a mean of μ and a standard deviation of σ.Let
₁ be the mean of a sample of 16 observations randomly chosen from this population,and
₂ be the mean of a sample of 25 observations randomly chosen from the same population.
Evaluate the statement P(μ - 0.2σ <
₁ < μ + 0.2σ)< P(μ - 0.2σ <
₂ < μ + 0.2σ)as to whether it is true or false.Please state if you are unable to determine whether the statement is true or false.Support your answer.