Question 1

The ideal estimator has the greatest variance among all unbiased estimators.

Accepted Answer

A) True 
 B)False

Question 2

As the sample size gets larger, the standard error of the sampling distribution of the sample mean
gets larger as well.

Accepted Answer

A) True 
 B)False

Question 3

Which of the following describes what the property of unbiasedness means?

Accepted Answer

A) The sampling distribution in question has the smallest variation of all possible sampling distributions. 
B) The center of the sampling distribution is found at the population parameter that is being estimated. 
C) The shape of the sampling distribution is approximately normally distributed. 
D) The center of the sampling distribution is found at the population standard deviation.

Question 4

Sample statistics are random variables, because different samples can lead to different values of
the sample statistics.

Accepted Answer

A) True 
 B)False

Question 5

The term statistic refers to a population quantity, and the term parameter refers to a sample
quantity.

Accepted Answer

A) True 
 B)False

Question 6

Which of the following describes what the property of minimum variance means?

Accepted Answer

A) The center of the sampling distribution is found at the population standard deviation. 
B) The shape of the sampling distribution is approximately normally distributed. 
C) The center of the sampling distribution is found at the population parameter that is being estimated. 
D) The sampling distribution in question has the smallest variation of all possible unbiased sampling distributions.

Question 7

Consider the population described by the probability distribution below. $\begin{array}{c|c|c|c}
x & 3 & 5 & 7 \
\hline p(x) & .1 & .7 & .2
\end{array}$

a. Find $\mu$.
b. Find the sampling distribution of the sample mean $\bar { x }$ for a random sample of $n = 2$ measurements
from the distribution.
C. Show that $\bar { x }$ is an unbiased estimator of $\mu$.

Accepted Answer

The answer of Consider the population described by the probability...

Question 8

The standard error of the sampling distribution of the sample mean is equal to σ, the standard
deviation of the population.

Accepted Answer

A) True 
 B)False

Question 9

Suppose a random sample of $n = 64$ measurements is selected from a population with mean $\mu = 65$ and standard deviation $\sigma = 12$. Find the probability that $\bar { x }$ falls between $65.75$ an $68.75$.

Accepted Answer

The answer of Suppose a random sample of \(n =...

Question 10

$$\text { If } \bar { x } \text { is a good estimator for } \mu \text {, then we expect the values of } \bar { x } \text { to cluster around } \mu \text {. }$$

Accepted Answer

A) True 
 B)False

Question 11

Consider the population described by the probability distribution below. $\begin{array}{c|c|c|c}
x & 3 & 5 & 7 \
\hline p(x) & .1 & .7 & .2
\end{array}$

a. Find $\sigma ^ { 2 }$.
b. Find the sampling distribution of the sample variance $s ^ { 2 }$ for a random sample of $n = 2$ measurements
from the distribution.
c. Show that $s ^ { 2 }$ is an unbiased estimator of $\sigma ^ { 2 }$.

Accepted Answer

The answer of Consider the population described by the probability...

Question 12

When estimating the population mean, the sample mean is always a better estimate than the
sample median.

Accepted Answer

A) True 
 B)False

Question 13

The Central Limit Theorem guarantees that the population is normal whenever n is sufficiently
large.

Accepted Answer

A) True 
 B)False

Question 14

The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal under certain conditions. Which of the following is a necessary condition
For the Central Limit Theorem to be used?

Accepted Answer

A) The population from which we are sampling must be normally distributed. 
B) The population size must be large . 
C) The sample size must be large . 
D) The population from which we are sampling must not be normally distributed.

Question 15

A random sample of $\mathrm { n } = 300$ measurements is drawn from a binomial population with probability of success . 43 . Give the mean and the standard deviation of the sampling distribution of the sample proportion, $\mathrm { p }$.

Accepted Answer

A)  $57 ; .014$ 
B)  .43;.029 
C)  $57 ; .029$ 
D)  .43;.014

Question 16

Suppose a random sample of $n = 64$ measurements is selected from a population with mean $\mu = 65$ and standard deviation $\sigma = 12$. Find the $z$-score corresponding to a value of $\bar { x }$ $= 68$.

Accepted Answer

The answer of Suppose a random sample of \(n =...

Question 17

The average score of all golfers for a particular course has a mean of 61 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the
49 golfers exceeded 62.

Accepted Answer

A) .4772 
B) .0228 
C) .1293 
D) .3707

Question 18

The probability distribution shown below describes a population of measurements. $\begin{array}{c|ccc}
\mathrm{x} & 0 & 2 & 4 \
\hline \mathrm{p}(\mathrm{x}) & 1 / 3 & 1 / 3 & 1 / 3
\end{array}$

Suppose that we took repeated random samples of $n = 2$ observations from the population described above. Which of the following would represent the sampling distribution of the sample mean?

Accepted Answer

A)  $\begin{array}{c|ccc}
\bar{x} & 0 & 2 & 4 \
\hline p(\bar{x}) & 1 / 3 & 1 / 3 & 1 / 3
\end{array}$ 
B)  $\begin{array}{c|ccccc}
\bar{x} & 0 & 1 & 2 & 3 & 4 \
\hline \mathrm{p}(\bar{x}) & 2 / 9 & 2 / 9 & 1 / 9 & 2 / 9 & 2 / 9
\end{array}$ 
C) $\begin{array}{c|ccccc}
\overline{\mathrm{x}} & 0 & 1 & 2 & 3 & 4 \
\hline \mathrm{p}(\overline{\mathrm{x}}) & 1 / 9 & 2 / 9 & 3 / 9 & 2 / 9 & 1 / 9
\end{array}$ 
D) $\begin{array}{c|ccccc}
\overline{\mathrm{x}} & 0 & 1 & 2 & 3 & 4 \
\hline \mathrm{p}(\overline{\mathrm{x})} & 1 / 5 & 1 / 5 & 1 / 5 & 1 / 5 & 1 / 5
\end{array}$

Question 19

Suppose a random sample of $n = 36$ measurements is selected from a population with mean $\mu = 256$ and variance $\sigma ^ { 2 } = 144$. Find the mean and standard deviation of the sampling distribution of the sample mean $\bar { x }$.

Accepted Answer

The answer of Suppose a random sample of \(n =...

Question 20

The sampling distribution of a sample statistic calculated from a sample of n measurements is the
probability distribution of the statistic.

Accepted Answer

A) True 
 B)False

Exam 6: Sampling Distributions

The ideal estimator has the greatest variance among all unbiased estimators.

As the sample size gets larger, the standard error of the sampling distribution of the sample mean gets larger as well.

Which of the following describes what the property of unbiasedness means?

Sample statistics are random variables, because different samples can lead to different values of the sample statistics.

The term statistic refers to a population quantity, and the term parameter refers to a sample quantity.

Which of the following describes what the property of minimum variance means?

The standard error of the sampling distribution of the sample mean is equal to σ, the standard deviation of the population.

Suppose a random sample of $n = 64$ measurements is selected from a population with mean $\mu = 65$ and standard deviation $\sigma = 12$ . Find the probability that $\bar { x }$ falls between $65.75$ an $68.75$ .

$\text { If } \bar { x } \text { is a good estimator for } \mu \text {, then we expect the values of } \bar { x } \text { to cluster around } \mu \text {. }$

When estimating the population mean, the sample mean is always a better estimate than the sample median.

The Central Limit Theorem guarantees that the population is normal whenever n is sufficiently large.

The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal under certain conditions. Which of the following is a necessary condition For the Central Limit Theorem to be used?

A random sample of $\mathrm { n } = 300$ measurements is drawn from a binomial population with probability of success . 43 . Give the mean and the standard deviation of the sampling distribution of the sample proportion, $\mathrm { p }$ .

Suppose a random sample of $n = 64$ measurements is selected from a population with mean $\mu = 65$ and standard deviation $\sigma = 12$ . Find the $z$ -score corresponding to a value of $\bar { x }$ $= 68$ .

The average score of all golfers for a particular course has a mean of 61 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 62.

Suppose a random sample of $n = 36$ measurements is selected from a population with mean $\mu = 256$ and variance $\sigma ^ { 2 } = 144$ . Find the mean and standard deviation of the sampling distribution of the sample mean $\bar { x }$ .

The sampling distribution of a sample statistic calculated from a sample of n measurements is the probability distribution of the statistic.

Exam 6: Sampling Distributions

The ideal estimator has the greatest variance among all unbiased estimators.

As the sample size gets larger, the standard error of the sampling distribution of the sample mean gets larger as well.

Which of the following describes what the property of unbiasedness means?

Sample statistics are random variables, because different samples can lead to different values of the sample statistics.

The term statistic refers to a population quantity, and the term parameter refers to a sample quantity.

Which of the following describes what the property of minimum variance means?

The standard error of the sampling distribution of the sample mean is equal to σ, the standard deviation of the population.

Suppose a random sample of n=64n = 64n=64 measurements is selected from a population with mean μ=65\mu = 65μ=65 and standard deviation σ=12\sigma = 12σ=12 . Find the probability that xˉ\bar { x }xˉ falls between 65.7565.7565.75 an 68.7568.7568.75 .

When estimating the population mean, the sample mean is always a better estimate than the sample median.

The Central Limit Theorem guarantees that the population is normal whenever n is sufficiently large.

The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal under certain conditions. Which of the following is a necessary condition For the Central Limit Theorem to be used?

A random sample of n=300\mathrm { n } = 300n=300 measurements is drawn from a binomial population with probability of success . 43 . Give the mean and the standard deviation of the sampling distribution of the sample proportion, p\mathrm { p }p .

Suppose a random sample of n=64n = 64n=64 measurements is selected from a population with mean μ=65\mu = 65μ=65 and standard deviation σ=12\sigma = 12σ=12 . Find the zzz -score corresponding to a value of xˉ\bar { x }xˉ =68= 68=68 .

The average score of all golfers for a particular course has a mean of 61 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 62.

Suppose a random sample of n=36n = 36n=36 measurements is selected from a population with mean μ=256\mu = 256μ=256 and variance σ2=144\sigma ^ { 2 } = 144σ2=144 . Find the mean and standard deviation of the sampling distribution of the sample mean xˉ\bar { x }xˉ .

The sampling distribution of a sample statistic calculated from a sample of n measurements is the probability distribution of the statistic.

Suppose a random sample of $n = 64$ measurements is selected from a population with mean $\mu = 65$ and standard deviation $\sigma = 12$ . Find the probability that $\bar { x }$ falls between $65.75$ an $68.75$ .

A random sample of $\mathrm { n } = 300$ measurements is drawn from a binomial population with probability of success . 43 . Give the mean and the standard deviation of the sampling distribution of the sample proportion, $\mathrm { p }$ .

Suppose a random sample of $n = 64$ measurements is selected from a population with mean $\mu = 65$ and standard deviation $\sigma = 12$ . Find the $z$ -score corresponding to a value of $\bar { x }$ $= 68$ .

Suppose a random sample of $n = 36$ measurements is selected from a population with mean $\mu = 256$ and variance $\sigma ^ { 2 } = 144$ . Find the mean and standard deviation of the sampling distribution of the sample mean $\bar { x }$ .