Question 1

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

Accepted Answer

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. 
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 2

Consider an infinite population with a mean of 100 and a standard deviation of 20. A random sample of size 50 is taken from this population. The standard deviation of the sample mean equals 3.2.

Accepted Answer

A) True 
 B)False

Question 3

The standard error of the mean is the standard deviation of the sampling distribution of $\bar { X }$ .

Accepted Answer

A) True 
 B)False

Question 4

The following table gives the number of pets owned for a population of four families. $$\begin{array} { | l | c | c | c | c | } 
\hline \text { Family } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } \
\hline \text { Number of pets owned } & 2 & 1 & 4 & 3 \
\hline
\end{array}$$ List all possible samples of two families that can be selected without replacement from this population, and compute the sample mean $\overline  { x } $ for each sample.

Accepted Answer

\[\begin{array} { | c | c | c | c | c |

Question 5

The following table gives the number of pets owned for a population of four families. $$\begin{array} { | l | c | c | c | c | } 
\hline \text { Family } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } \
\hline \text { Number of pets owned } & 2 & 1 & 4 & 3 \
\hline
\end{array}$$ Find the mean and standard deviation for the population.

Accepted Answer

The answer of The following table gives the number of...

Question 6

Suppose that the time needed to complete a final exam is normally distributed with a mean of 85 minutes and a standard deviation of 18 minutes.
a. What is the probability that the total time taken by a group of 100 students will not exceed 8200 minutes?
b. What assumption did you have to make in your computations in part (a)?

Accepted Answer

a. 0.0475.
b. It is necessary

Question 7

The finite population correction factor should not be used when:

Accepted Answer

A)  we are sampling from an infinite population. 
B)  we are sampling from a finite population. 
C)  sample size is greater than 1% of the population size. 
D)  None of these choices are correct. 
A)  we are sampling from an infinite population. 
B)  we are sampling from a finite population. 
C)  sample size is greater than 1% of the population size. 
D)  None of these choices are correct.

Question 8

A sample of size 50 is to be taken from an infinite population whose mean and standard deviation are 52 and 20, respectively. The probability that the sample mean will be larger than 49 is:

Accepted Answer

A)  0.4452. 
B)  0.9452. 
C)  0.8554. 
D)  0.3554. 
A)  0.4452. 
B)  0.9452. 
C)  0.8554. 
D)  0.3554.

Question 9

The amount of time spent by Australian adults playing sports per day is normally distributed, with a mean of 4 hours and standard deviation of 1.25 hours. Use this information to answer the following question(s).
Find the probability that a randomly selected Australian adult plays sport for more than 5 hours per day.

Accepted Answer

The answer of The amount of time spent by Australian...

Question 10

If all possible samples of size n are drawn from an infinite population with mean$\mu$and standard deviation $\sigma$, then the standard error of the sample mean is inversely proportional to:

Accepted Answer

A)  $\mu$ 
B)  $\sigma$ 
C)  n. 
D)  $\sqrt { n }$ . 
A)  $\mu$ 
B)  $\sigma$ 
C)  n. 
D)  $\sqrt { n }$ .

Question 11

Assume that the time needed by a worker to perform a maintenance operation is normally distributed, with a mean of 60 minutes and a standard deviation of 6 minutes. What is the probability that the average time needed by a sample of 5 workers to perform the maintenance is between 63 and 68 minutes?

Accepted Answer

The answer of Assume that the time needed by a...

Question 12

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 45 and 9, respectively. The mean and standard error of the sampling distribution of the sample mean are:

Accepted Answer

A)  9 and 45. 
B)  45 and 9. 
C)  81 and 45. 
D)  45 and 1. 
A)  9 and 45. 
B)  45 and 9. 
C)  81 and 45. 
D)  45 and 1.

Question 13

An infinite population has a mean of 120 and a standard deviation of 44. A sample of 100 observations is to be selected at random from the population.
a. What is the expected value of the sample mean?
b. What is the standard deviation of the sample mean?
c. What is the shape of the sampling distribution of the sample mean?
d. What does the sampling distribution of the sample mean show?

Accepted Answer

a. 120.
b. 4.4.
c. Approximately normal,

Question 14

As a general rule in computing the standard error of the sample mean, the finite population correction factor is used only if the:

Accepted Answer

A)  sample size is smaller than 10% of the population size. 
B)  population size is smaller than 10% of the sample size. 
C)  sample size is greater than 1% of the population size. 
D)  population size is greater than 1% of the sample size. 
A)  sample size is smaller than 10% of the population size. 
B)  population size is smaller than 10% of the sample size. 
C)  sample size is greater than 1% of the population size. 
D)  population size is greater than 1% of the sample size.

Question 15

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. If the population of women's heights were not normally distributed, which, if any, of the following questions could you answer?
a. What is the probability that a randomly selected woman is taller than 160 cm?
b. A random sample of five women is selected. What is the probability that the sample mean is greater than 160 cm?
c. What is the probability that the mean height of a random sample of 75 women is greater than 160 cm?

Accepted Answer

We could answer part

Question 16

If it is known that the population proportion of car parks in a particular city that offer early discount fees is 25%, which of the following best describes the mean and standard deviation of the sampling distribution of the sample proportion of car parks that offer early discount fees for samples taken of size 30?

Accepted Answer

A)  The mean is 0.25 and the standard deviation is 0.006. 
B)  The mean is 0.25 and the standard deviation is 0.75. 
C)  The mean is 0.25 and the standard deviation is 0.079. 
D)  None of these choices are correct. 
A)  The mean is 0.25 and the standard deviation is 0.006. 
B)  The mean is 0.25 and the standard deviation is 0.75. 
C)  The mean is 0.25 and the standard deviation is 0.079. 
D)  None of these choices are correct.

Question 17

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. Use this information to answer the following question(s).
What is the probability that a randomly selected woman is shorter than 162 centimetres?

Accepted Answer

The answer of The heights of women in Australia are...

Question 18

A sample of size 70 is selected at random from a finite population. If the finite population correction factor is 0.808, the population size (rounded to the nearest integer) must be 200.

Accepted Answer

A) True 
 B)False

Question 19

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean $\bar { X }$ is referred to as the normal distribution.

Accepted Answer

A) True 
 B)False

Question 20

A sample of size 400 is drawn from a population whose mean and variance are 5000 and 10 000, respectively. Find the following probabilities.
a. P( $\bar { X }$ < 4,990).
b. P(4995 < $\bar { X }$ < 5010).
c. P( $\bar { X }$ = 5000).

Accepted Answer

a. 0.0228.

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

Consider an infinite population with a mean of 100 and a standard deviation of 20. A random sample of size 50 is taken from this population. The standard deviation of the sample mean equals 3.2.

The standard error of the mean is the standard deviation of the sampling distribution of $\bar { X }$ .

The following table gives the number of pets owned for a population of four families. Family Number of pets owned 2 1 4 3 List all possible samples of two families that can be selected without replacement from this population, and compute the sample mean $\overline { x }$ for each sample.

The following table gives the number of pets owned for a population of four families. Family Number of pets owned 2 1 4 3 Find the mean and standard deviation for the population.

The finite population correction factor should not be used when:

A sample of size 50 is to be taken from an infinite population whose mean and standard deviation are 52 and 20, respectively. The probability that the sample mean will be larger than 49 is:

If all possible samples of size n are drawn from an infinite population with mean $\mu$ and standard deviation $\sigma$ , then the standard error of the sample mean is inversely proportional to:

Assume that the time needed by a worker to perform a maintenance operation is normally distributed, with a mean of 60 minutes and a standard deviation of 6 minutes. What is the probability that the average time needed by a sample of 5 workers to perform the maintenance is between 63 and 68 minutes?

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 45 and 9, respectively. The mean and standard error of the sampling distribution of the sample mean are:

As a general rule in computing the standard error of the sample mean, the finite population correction factor is used only if the:

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. Use this information to answer the following question(s). What is the probability that a randomly selected woman is shorter than 162 centimetres?

A sample of size 70 is selected at random from a finite population. If the finite population correction factor is 0.808, the population size (rounded to the nearest integer) must be 200.

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean $\bar { X }$ is referred to as the normal distribution.

A sample of size 400 is drawn from a population whose mean and variance are 5000 and 10 000, respectively. Find the following probabilities. a. P( $\bar { X }$ < 4,990). b. P(4995 < $\bar { X }$ < 5010). c. P( $\bar { X }$ = 5000).

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 10: Sampling Distributions

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

Consider an infinite population with a mean of 100 and a standard deviation of 20. A random sample of size 50 is taken from this population. The standard deviation of the sample mean equals 3.2.

The standard error of the mean is the standard deviation of the sampling distribution of Xˉ\bar { X }Xˉ .

The following table gives the number of pets owned for a population of four families. Family Number of pets owned 2 1 4 3 List all possible samples of two families that can be selected without replacement from this population, and compute the sample mean x‾\overline { x } x for each sample.

The following table gives the number of pets owned for a population of four families. Family Number of pets owned 2 1 4 3 Find the mean and standard deviation for the population.

The finite population correction factor should not be used when:

A sample of size 50 is to be taken from an infinite population whose mean and standard deviation are 52 and 20, respectively. The probability that the sample mean will be larger than 49 is:

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

Assume that the time needed by a worker to perform a maintenance operation is normally distributed, with a mean of 60 minutes and a standard deviation of 6 minutes. What is the probability that the average time needed by a sample of 5 workers to perform the maintenance is between 63 and 68 minutes?

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 45 and 9, respectively. The mean and standard error of the sampling distribution of the sample mean are:

As a general rule in computing the standard error of the sample mean, the finite population correction factor is used only if the:

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. Use this information to answer the following question(s). What is the probability that a randomly selected woman is shorter than 162 centimetres?

A sample of size 70 is selected at random from a finite population. If the finite population correction factor is 0.808, the population size (rounded to the nearest integer) must be 200.

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean Xˉ\bar { X }Xˉ is referred to as the normal distribution.

A sample of size 400 is drawn from a population whose mean and variance are 5000 and 10 000, respectively. Find the following probabilities. a. P( Xˉ\bar { X }Xˉ < 4,990). b. P(4995 < Xˉ\bar { X }Xˉ < 5010). c. P( Xˉ\bar { X }Xˉ = 5000).

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

The standard error of the mean is the standard deviation of the sampling distribution of $\bar { X }$ .

The following table gives the number of pets owned for a population of four families. Family Number of pets owned 2 1 4 3 List all possible samples of two families that can be selected without replacement from this population, and compute the sample mean $\overline { x }$ for each sample.

If all possible samples of size n are drawn from an infinite population with mean $\mu$ and standard deviation $\sigma$ , then the standard error of the sample mean is inversely proportional to:

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean $\bar { X }$ is referred to as the normal distribution.

A sample of size 400 is drawn from a population whose mean and variance are 5000 and 10 000, respectively. Find the following probabilities. a. P( $\bar { X }$ < 4,990). b. P(4995 < $\bar { X }$ < 5010). c. P( $\bar { X }$ = 5000).