Question 1

The finite population correction is not needed if the population size is large relative to the sample size.As a rule of thumb,we will treat any population that is at least ____________________ times larger than the sample size as large.

Accepted Answer

The answer of The finite population correction is not needed...

Question 2

Suppose the ages of students in your program follow a positively skewed distribution with mean of 24 years and a standard deviation of 4 years.If we randomly sampled 100 students,which of the following statements about the sampling distribution of the sample mean age is NOT true?

Accepted Answer

A)  The mean of the sampling distribution of sample mean is equal to 24 years. 
B)  The standard deviation of the sampling distribution of sample mean is equal to 4 years. 
C)  The shape of the sampling distribution of sample mean is approximately normal. 
D)  All of these choices are true.

Question 3

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed,with a mean of 3.2 pounds and standard deviation of 0.84 pounds.If a sample of 16 fish is taken,what is the standard error of the mean weight?

Accepted Answer

A)  0.840 
B)  0.053 
C)  0.210 
D)  None of these choices.

Question 4

If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85,and standard deviations 12 and 15,respectively,then the mean of the difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is equal to:

Accepted Answer

A)  -7 
B)  7 
C)  (78 -85)/ (30 - 36)= 1.17 
D)  78/30 - 85/36 = 0.24

Question 5

As the size of the sample is increased,the standard error of $\bar { X }$ decreases.

Accepted Answer

A) True 
 B)False

Question 6

CFO's Salary
Suppose that the starting salaries of female CFO's have a positively skewed distribution with mean of $56,000 and a standard deviation of $12,000.The starting salaries of male CFO's are positively skewed with a mean of $50,000 and a standard deviation of $10,000.A random sample of 50 female CFO's and a random sample of 40 male CFO's are selected.
-{CFO's Salary Narrative} What is the sampling distribution of the sample mean difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ ? Explain.

Accepted Answer

The answer of CFO's Salary
Suppose that the starting salaries of...

Question 7

Magazines
A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation.
-{Magazines Narrative} What is the shape of the sampling distribution of the sample mean number of magazines sold per day? Why?

Accepted Answer

The answer of Magazines
A local magazine store sells an average...

Question 8

Number of Fish Tanks
The following data give the number of fish tanks owned for a population of 4 families.
 $$\begin{array} { | l | c c c c | } 
\hline \text { Family } & \text { A } & \text { B } & \text { C } & \text { D } \
\hline \text { Number af Fish Tanks Owned } & 2 & 1 & 4 & 3 \
\hline
\end{array}$$
-{Number of Fish Tanks Narrative} List all possible samples of 2 families that can be selected without replacement from this population,and compute the sample mean $\bar { X }$ for each sample.

Accepted Answer

The answer of Number of Fish Tanks
The following data give...

Question 9

Retirees
A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years,respectively.
-{Retirees Narrative} What is the probability that the mean age is at most 73 years?

Accepted Answer

The answer of Retirees
A sample of 50 retirees is drawn...

Question 10

Heights of Fences
Heights of fences are normally distributed with a mean of 52 inches and a standard deviation of 4 inches.
-{Heights of Fences Narrative} Find the probability that one randomly selected fence is under 54 inches.

Accepted Answer

The answer of Heights of Fences
Heights of fences are normally...

Question 11

Magazines
A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation.
-{Magazines Narrative} Find the expected value and the standard error of the sample mean.

Accepted Answer

The answer of Magazines
A local magazine store sells an average...

Question 12

In general,the binomial probability P(X $\le$ x)is approximated by the area under the normal curve to the left of x + .5.

Accepted Answer

A) True 
 B)False

Question 13

College Dean
A college dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200.
-Consider an infinite population with a mean of 100 and a standard deviation of 20.A random sample of size 64 is taken from this population.The standard deviation of the sample mean equals 2.50.

Accepted Answer

A) True 
 B)False

Question 14

Barack Obama
Bill Clinton,the former President of the United States,believes that the proportion of voters who will vote for Barack Obama in the year 2012 presidential elections is 0.65.A sample of 500 voters is selected at random.
-{Barack Obama Narrative} What is the probability that the number of voters in the sample who will vote for Barack Obama in the year 2012 is between 340 and 350?

Accepted Answer

The answer of Barack Obama
Bill Clinton,the former President of the...

Question 15

Retirees
A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years,respectively.
-(Retirees Narrative} Find the mean and standard error of the sampling distribution of the sample mean.

Accepted Answer

The answer of Retirees
A sample of 50 retirees is drawn...

Question 16

If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85,and standard deviations 12 and 15,respectively,then the standard error of the difference $\bar { X } _ { 1 }$ and $\bar { X } _ { 2 }$ is equal to:

Accepted Answer

A)  0.904 
B)  3.324 
C)  3.391 
D)  0.833

Question 17

Consider an infinite population with a mean of 160 and a standard deviation of 25.A random sample of size 64 is taken from this population.The standard deviation of the sample mean equals:

Accepted Answer

A)  25 
B)  25/64 
C)  25/$\surd$64 
D)  None of these choices.

Question 18

The standard deviation of $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is also called the:

Accepted Answer

A)  standard error of the difference between two sample means. 
B)  standard deviation of the difference between the population means. 
C)  normal approximation to the difference of two binomial random variables. 
D)  None of these choices.

Question 19

A CPA knows from past history that the average accounts receivable for a company is $521.72 with a standard deviation of $584.64.If the auditor takes a simple random sample of 100 accounts,what is the probability that the mean of the sample is within $120 of the population mean?

Accepted Answer

The answer of A CPA knows from past history that...

Question 20

College Dean
A college dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200.
-A sample of size n is selected at random from an infinite population.As n increases,the standard error of the sample mean increases.

Accepted Answer

A) True 
 B)False

Exam 9: Sampling Distributions

The finite population correction is not needed if the population size is large relative to the sample size.As a rule of thumb,we will treat any population that is at least ____________________ times larger than the sample size as large.

Suppose the ages of students in your program follow a positively skewed distribution with mean of 24 years and a standard deviation of 4 years.If we randomly sampled 100 students,which of the following statements about the sampling distribution of the sample mean age is NOT true?

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed,with a mean of 3.2 pounds and standard deviation of 0.84 pounds.If a sample of 16 fish is taken,what is the standard error of the mean weight?

If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85,and standard deviations 12 and 15,respectively,then the mean of the difference Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​ is equal to:

As the size of the sample is increased,the standard error of Xˉ\bar { X }Xˉ decreases.

Magazines A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation. -{Magazines Narrative} What is the shape of the sampling distribution of the sample mean number of magazines sold per day? Why?

Retirees A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years,respectively. -{Retirees Narrative} What is the probability that the mean age is at most 73 years?

Heights of Fences Heights of fences are normally distributed with a mean of 52 inches and a standard deviation of 4 inches. -{Heights of Fences Narrative} Find the probability that one randomly selected fence is under 54 inches.

Magazines A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation. -{Magazines Narrative} Find the expected value and the standard error of the sample mean.

In general,the binomial probability P(X ≤\le≤ x)is approximated by the area under the normal curve to the left of x + .5.

Retirees A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years,respectively. -(Retirees Narrative} Find the mean and standard error of the sampling distribution of the sample mean.

If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85,and standard deviations 12 and 15,respectively,then the standard error of the difference Xˉ1\bar { X } _ { 1 }Xˉ1​ and Xˉ2\bar { X } _ { 2 }Xˉ2​ is equal to:

Consider an infinite population with a mean of 160 and a standard deviation of 25.A random sample of size 64 is taken from this population.The standard deviation of the sample mean equals:

The standard deviation of Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​ is also called the:

A CPA knows from past history that the average accounts receivable for a company is $521.72 with a standard deviation of $584.64.If the auditor takes a simple random sample of 100 accounts,what is the probability that the mean of the sample is within $120 of the population mean?

College Dean A college dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200. -A sample of size n is selected at random from an infinite population.As n increases,the standard error of the sample mean increases.

If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85,and standard deviations 12 and 15,respectively,then the mean of the difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is equal to:

As the size of the sample is increased,the standard error of $\bar { X }$ decreases.

In general,the binomial probability P(X $\le$ x)is approximated by the area under the normal curve to the left of x + .5.

If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85,and standard deviations 12 and 15,respectively,then the standard error of the difference $\bar { X } _ { 1 }$ and $\bar { X } _ { 2 }$ is equal to:

The standard deviation of $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is also called the: