Question 1

If the population is divided into relatively small subdivisions and then some of these subdivisions are selected for inclusion in the overall sample, the method is called _______ sampling.
A) stratified
B) cluster
C) quota
D) systematic

Accepted Answer

Cluster sampling involves dividing the population into separate groups, known as clusters, and then a simple random sample of these clusters is selected. If all elements within the selected clusters are included in the sample, it is a single-stage cluster sampling. This method is used when it is costly or impractical to conduct a list of the entire population.

Question 2

The possible presence of hidden periodicities is a danger of _______ sampling.
A) stratified
B) cluster
C) simple random
D) systematic

Accepted Answer

Systematic sampling can introduce bias if there is a hidden periodicity in the order of the population that aligns with the sampling interval, leading to over- or under-representation of certain patterns.

Question 3

The standard error of the mean of a sample of 100 items from a population will be equal to _______ times the standard error of the mean of 25 items.
A) $\frac{1}{4}$
B) $\frac{1}{2}$
C) 4
D) 2

Accepted Answer

The standard error of the mean (SEM) is inversely proportional to the square root of the sample size (n). Therefore, when the sample size increases from 25 to 100, the square root of the sample size increases by a factor of 2 (sqrt(100)/sqrt(25) = 10/5 = 2), making the SEM 1/2 times the original SEM.

Question 4

The value we use for the standard error of the mean when $n$ is at least $5 \%$ of the population size is
A) $\frac{\sigma}{\sqrt{n}} \sqrt{\frac{N-n}{N-1}}$.
B) $\sigma$.
C) $\frac{\sigma}{\sqrt{n}}$.
D) $s$.

Accepted Answer

The correct formula for the standard error of the mean when the sample size $n$ is at least $5\%$ of the population size $N$ includes a correction factor to account for the finite population size, which is given by $\frac{\sigma}{\sqrt{n}} \sqrt{\frac{N-n}{N-1}}$. This adjustment is known as the finite population correction (FPC).

Question 5

If the digits $0,2,4,6$, and 8 represent heads and the digits 1, 3, 5, 7, and 9 represent tails, then the random numbers 527, 648, 910, and 485 represent what sequence of numbers of heads in four flips of three coins?
A) $2,1,1,3$
B) $2,2,1,3$
C) $2,0,2,1$
D) $1,3,1,2$

Accepted Answer

The answer of If the digits $0,2,4,6$, and 8 represent...

Question 6

Suppose we obtain a sample mean of 80 from a sample of size 100 from an infinite population with $\sigma=50$. Then the probability is 0.75 that the error in estimating the population mean using Chebyshev's theorem is:
A) between 30 and 130 .
B) less than 6.
C) between 74 and 86 .
D) less than 10 .

Accepted Answer

Chebyshev's theorem states that for any distribution, the probability that a value lies within k standard deviations of the mean is at least $1 - \frac{1}{k^2}$. Here, the standard error is $\frac{\sigma}{\sqrt{n}} = \frac{50}{10} = 5$. For a probability of 0.75, $1 - \frac{1}{k^2} = 0.75$, solving gives $k \approx 2$. Thus, the error is less than $2 \times 5 = 10$.

Question 7

Our sample size criterion for applying the central limit theorem if the population may not be normal is
A) $n \geq 30$.
B) $n \geq 0.05 \mathrm{~N}$.
C) $n<0.05 \mathrm{~N}$.
D) $n \geq 5$.

Accepted Answer

The central limit theorem states that, for sufficiently large sample sizes (usually $n \geq 30$), the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution.

Question 8

The central limit theorem can be used to estimate the
A) population mean from the sample mean.
B) probability of error in using $\bar{x}$ to estimate $\mu$.
C) mean of the sampling distribution by using the population mean.
D) standard error of the mean by using $\sigma$.

Accepted Answer

The answer of The central limit theorem can be used...

Question 9

An important goal of _______ sampling is that there is less variability within the resulting subgroups than in the entire population.
A) stratified
B) cluster
C) quota
D) systematic

Accepted Answer

Stratified sampling aims to reduce variability within subgroups by dividing the population into smaller, distinct groups (strata) before sampling. This ensures that the sample more accurately reflects the population's diversity.

Question 10

A stratified sample is taken from a population of size $N=2000$ which consists of two strata of $N_{1}=800$, $N_{2}=1200, n_{1}=20, n_{2}=40, \sigma_{1}=3, \sigma_{2}=5$. Then the method of allocation is
A) proportional.
B) optimum.
C) neither proportional nor optimum.
D) both proportional and optimum.

Accepted Answer

The answer of A stratified sample is taken from a...

Question 11

If the mean of a random sample of size 400 is used to estimate the mean of an infinite population with a standard deviation of 60 , the probability is 0.95 that the error is less than
A) 1.96 .
B) 117.6 .
C) 3.92 .
D) 5.88 .

Accepted Answer

The margin of error in estimating the population mean with a 95% confidence level is given by $Z \times \frac{\sigma}{\sqrt{n}}$, where $Z$ is the Z-score corresponding to the confidence level (1.96 for 95%), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the values: $1.96 \times \frac{60}{\sqrt{400}} = 1.96 \times 3 = 5.88$.

Question 12

If we want to change a standard error from 12 to 4 by changing the sample size, we need to multiply the original sample size by
A) 3 .
B) 9 .
C) $\frac{1}{3}$.
D) $\frac{1}{9}$.

Accepted Answer

The standard error of the mean is inversely proportional to the square root of the sample size (n). To reduce the standard error from 12 to 4, which is a factor of 3, we need to increase the sample size by a factor of 3^2 = 9, because the relationship is squared.

Question 13

Write the word or phrase that best completes each statement or answers the question.
-How many different samples of size 2 can be selected from a population of size 15 ?

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Write the word or phrase that best completes each statement or answers the question.
-How many different samples of size 3 can be selected from a population of 12 ?

Accepted Answer

The answer of Write the word or phrase that best...

Question 15

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining.
-In how many ways can the investor select two stocks to buy?

Accepted Answer

The answer of An investor considers investing in the stocks...

Question 16

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining.
-In how many ways can the investor select three stocks to buy?

Accepted Answer

The answer of An investor considers investing in the stocks...

Question 17

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining.
-Find the probability of selecting any particular sample of two stocks.

Accepted Answer

The answer of An investor considers investing in the stocks...

Question 18

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining.
-Find the probability of any particular one of the companies being included in a sample of two stocks.

Accepted Answer

The answer of An investor considers investing in the stocks...

Question 19

Random samples of size 2 are selected from the finite population which consists of the numbers 4, 7, 10, 13, 16, and 19.
-Find the mean and standard deviation of this population.

Accepted Answer

The answer of Random samples of size 2 are selected...

Question 20

Random samples of size 2 are selected from the finite population which consists of the numbers 4, 7, 10, 13, 16, and 19.
-List the 15 possible random samples of size 2 that can be selected from the finite population, and calculate their means.

Accepted Answer

The answer of Random samples of size 2 are selected...

Quiz 10: Sampling and Sampling Distributions

If the population is divided into relatively small subdivisions and then some of these subdivisions are selected for inclusion in the overall sample, the method is called _______ sampling.

The possible presence of hidden periodicities is a danger of _______ sampling.

The standard error of the mean of a sample of 100 items from a population will be equal to _______ times the standard error of the mean of 25 items.

The value we use for the standard error of the mean when $n$ is at least $5 \%$ of the population size is

If the digits $0,2,4,6$ , and 8 represent heads and the digits 1, 3, 5, 7, and 9 represent tails, then the random numbers 527, 648, 910, and 485 represent what sequence of numbers of heads in four flips of three coins?

Suppose we obtain a sample mean of 80 from a sample of size 100 from an infinite population with $\sigma=50$ . Then the probability is 0.75 that the error in estimating the population mean using Chebyshev's theorem is:

Our sample size criterion for applying the central limit theorem if the population may not be normal is

The central limit theorem can be used to estimate the

An important goal of _______ sampling is that there is less variability within the resulting subgroups than in the entire population.

A stratified sample is taken from a population of size $N=2000$ which consists of two strata of $N_{1}=800$ , $N_{2}=1200, n_{1}=20, n_{2}=40, \sigma_{1}=3, \sigma_{2}=5$ . Then the method of allocation is

If the mean of a random sample of size 400 is used to estimate the mean of an infinite population with a standard deviation of 60 , the probability is 0.95 that the error is less than

If we want to change a standard error from 12 to 4 by changing the sample size, we need to multiply the original sample size by

Write the word or phrase that best completes each statement or answers the question. -How many different samples of size 2 can be selected from a population of size 15 ?

Write the word or phrase that best completes each statement or answers the question. -How many different samples of size 3 can be selected from a population of 12 ?

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining. -In how many ways can the investor select two stocks to buy?

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining. -In how many ways can the investor select three stocks to buy?

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining. -Find the probability of selecting any particular sample of two stocks.

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining. -Find the probability of any particular one of the companies being included in a sample of two stocks.

Random samples of size 2 are selected from the finite population which consists of the numbers 4, 7, 10, 13, 16, and 19. -Find the mean and standard deviation of this population.

Random samples of size 2 are selected from the finite population which consists of the numbers 4, 7, 10, 13, 16, and 19. -List the 15 possible random samples of size 2 that can be selected from the finite population, and calculate their means.

Quiz 10: Sampling and Sampling Distributions

If the population is divided into relatively small subdivisions and then some of these subdivisions are selected for inclusion in the overall sample, the method is called _______ sampling.

The possible presence of hidden periodicities is a danger of _______ sampling.

The standard error of the mean of a sample of 100 items from a population will be equal to _______ times the standard error of the mean of 25 items.

The value we use for the standard error of the mean when nnn is at least 5%5 \%5% of the population size is

If the digits 0,2,4,60,2,4,60,2,4,6 , and 8 represent heads and the digits 1, 3, 5, 7, and 9 represent tails, then the random numbers 527, 648, 910, and 485 represent what sequence of numbers of heads in four flips of three coins?

Suppose we obtain a sample mean of 80 from a sample of size 100 from an infinite population with σ=50\sigma=50σ=50 . Then the probability is 0.75 that the error in estimating the population mean using Chebyshev's theorem is:

Our sample size criterion for applying the central limit theorem if the population may not be normal is

The central limit theorem can be used to estimate the

An important goal of _______ sampling is that there is less variability within the resulting subgroups than in the entire population.

If the mean of a random sample of size 400 is used to estimate the mean of an infinite population with a standard deviation of 60 , the probability is 0.95 that the error is less than

If we want to change a standard error from 12 to 4 by changing the sample size, we need to multiply the original sample size by

Write the word or phrase that best completes each statement or answers the question. -How many different samples of size 2 can be selected from a population of size 15 ?

Write the word or phrase that best completes each statement or answers the question. -How many different samples of size 3 can be selected from a population of 12 ?

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining. -In how many ways can the investor select two stocks to buy?

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining. -In how many ways can the investor select three stocks to buy?

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining. -Find the probability of selecting any particular sample of two stocks.

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining. -Find the probability of any particular one of the companies being included in a sample of two stocks.

Random samples of size 2 are selected from the finite population which consists of the numbers 4, 7, 10, 13, 16, and 19. -Find the mean and standard deviation of this population.

Random samples of size 2 are selected from the finite population which consists of the numbers 4, 7, 10, 13, 16, and 19. -List the 15 possible random samples of size 2 that can be selected from the finite population, and calculate their means.

The value we use for the standard error of the mean when $n$ is at least $5 \%$ of the population size is

If the digits $0,2,4,6$ , and 8 represent heads and the digits 1, 3, 5, 7, and 9 represent tails, then the random numbers 527, 648, 910, and 485 represent what sequence of numbers of heads in four flips of three coins?

Suppose we obtain a sample mean of 80 from a sample of size 100 from an infinite population with $\sigma=50$ . Then the probability is 0.75 that the error in estimating the population mean using Chebyshev's theorem is: