Question 1

An unbiased estimator is a sample statistic whose expected value equals the population parameter.

Accepted Answer

A) True 
 B)False

Question 2

Is the sample mean a consistent estimator of the population mean? Explain

Accepted Answer

Yes, the mean is consistent be

Question 3

An engineer for an electric fencing company is interested in the mean length of wires being cut automatically by machine. The desired length of the wires is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. Suppose the engineer decided to estimate the mean length to within 0.025 with 99% confidence. What sample size would be needed?

Accepted Answer

n = 240 (u

Question 4

Explain briefly why interval estimators are preferred to point estimators.

Accepted Answer

An interval estimator incorpor

Question 5

To estimate with 95% confidence the mean of a normal population whose standard deviation is assumed to be 4 and the maximum allowable sampling error is assumed to be 1, requires a random sample of size 62.

Accepted Answer

A) True 
 B)False

Question 6

Because n is an integer and we want the bound on the error of estimation to be no more than a given amount, any non-integer value found for n must always be rounded ____________________.

Accepted Answer

The answer of Because n is an integer and we...

Question 7

Other things being equal, as the confidence level increases, the width of the confidence interval increases.

Accepted Answer

A) True 
 B)False

Question 8

Statisticians can control the ____________________ of a confidence interval by determining the sample size necessary to produce the desired results.

Accepted Answer

The answer of Statisticians can control the ____________________ of a...

Question 9

NARRBEGIN: Conference Rooms Rented
Conference Rooms Rented
A hotel chain wants to estimate the average number of conference rooms rented daily in each month. The population of conference rooms rented daily is assumed to be normally distributed for each with a standard deviation of 24 rooms.NARREND
-{Conference Rooms Rented Narrative} During January, a sample of 16 days has a sample mean of 48 rooms. This information is used to calculate an interval estimate for the population mean to be from 40 to 56 rooms. What is the level of confidence of this interval?

Accepted Answer

The answer of NARRBEGIN: Conference Rooms Rented
Conference Rooms Rented
A hotel...

Question 10

How large a sample of federal employees in Nevada should be taken if we want to estimate with 98% confidence the mean salary to within $2,000. The population standard deviation is assumed to be $10,500.

Accepted Answer

The answer of How large a sample of federal employees...

Question 11

NARRBEGIN: Time Spent Playing Comput
Time Spent Playing Computer Games
Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.NARREND
-{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean.

Accepted Answer

LCL = 6.21

Question 12

A precision control engineer is interested in the mean length of tubing being cut automatically by machine. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 60 cut tubes yields a mean length of 12.15 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine.
a.What is the z$\alpha$ / 2 value to use in obtaining the confidence interval?
b.Develop the 99% confidence interval for $\mu$.

Accepted Answer

a.z<sub>  / 2 </sub>

Question 13

The sample ____________________ is an unbiased estimator for the population mean.

Accepted Answer

The answer of The sample ____________________ is an unbiased estimator...

Question 14

An unbiased estimator of a population parameter is defined as:

Accepted Answer

A) an estimator whose expected value is equal to the parameter. 
B) an estimator whose variance is equal to one. 
C) an estimator whose expected value is equal to zero. 
D) an estimator whose variance goes to zero as the sample size goes to infinity. 
A) an estimator whose expected value is equal to the parameter. 
B) an estimator whose variance is equal to one. 
C) an estimator whose expected value is equal to zero. 
D) an estimator whose variance goes to zero as the sample size goes to infinity.

Question 15

Suppose that a 95% confidence interval for $\mu$ is given by $\bar { x } \pm 3.25$ . This notation means that, if we repeatedly draw samples of the same size from the same population, 95% of the values of $\bar { x }$ will be such that $\mu$would lie somewhere between $\bar { x } - 3.25$ and $\bar { x } + 3.25$ .

Accepted Answer

A) True 
 B)False

Question 16

In the formula $\bar { x } \pm z _ { a / 2 } \sigma / \sqrt { n }$ , the subscript$\alpha$ / 2 refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

Accepted Answer

A) True 
 B)False

Question 17

The term 1 - $\alpha$ refers to:

Accepted Answer

A) the probability that a confidence interval does not contain the population parameter. 
B) the confidence level. 
C) the level of unbiasedness. 
D) the level of consistency. 
A) the probability that a confidence interval does not contain the population parameter. 
B) the confidence level. 
C) the level of unbiasedness. 
D) the level of consistency.

Question 18

Which of the following conditions does not allow you to use the formula $\bar { x } \pm z _ { a / 2 } \sigma / \sqrt { n }$ to estimate $\mu$?

Accepted Answer

A) Population is normally distributed and the population variance is known. 
B) Population is not normally distributed but n is large; population variance is known. 
C) Population has any distribution and n is any size. 
D) All of these choices allow you to use the formula. 
A) Population is normally distributed and the population variance is known. 
B) Population is not normally distributed but n is large; population variance is known. 
C) Population has any distribution and n is any size. 
D) All of these choices allow you to use the formula.

Question 19

In determining the sample size n needed to estimate the population mean, n is higher if the population standard deviation $\sigma$ is higher.

Accepted Answer

A) True 
 B)False

Question 20

A 99% confidence interval estimate of the population mean $\mu$ can be interpreted to mean:

Accepted Answer

A) if all possible sample are taken and confidence intervals created, 99% of them would include the true population mean somewhere within their interval. 
B) we have 99% confidence that we have selected a sample whose interval does include the population mean. 
C) we estimate that the population mean falls between the lower and upper confidence limits, and this type of estimator is correct 99% of the time. 
D) All of these choices are true. 
A) if all possible sample are taken and confidence intervals created, 99% of them would include the true population mean somewhere within their interval. 
B) we have 99% confidence that we have selected a sample whose interval does include the population mean. 
C) we estimate that the population mean falls between the lower and upper confidence limits, and this type of estimator is correct 99% of the time. 
D) All of these choices are true.

An unbiased estimator is a sample statistic whose expected value equals the population parameter.

Is the sample mean a consistent estimator of the population mean? Explain

Explain briefly why interval estimators are preferred to point estimators.

To estimate with 95% confidence the mean of a normal population whose standard deviation is assumed to be 4 and the maximum allowable sampling error is assumed to be 1, requires a random sample of size 62.

Because n is an integer and we want the bound on the error of estimation to be no more than a given amount, any non-integer value found for n must always be rounded ____________________.

Other things being equal, as the confidence level increases, the width of the confidence interval increases.

Statisticians can control the ____________________ of a confidence interval by determining the sample size necessary to produce the desired results.

How large a sample of federal employees in Nevada should be taken if we want to estimate with 98% confidence the mean salary to within $2,000. The population standard deviation is assumed to be $10,500.

The sample ____________________ is an unbiased estimator for the population mean.

An unbiased estimator of a population parameter is defined as:

In the formula $\bar { x } \pm z _ { a / 2 } \sigma / \sqrt { n }$ , the subscript $\alpha$ / 2 refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

The term 1 - $\alpha$ refers to:

Which of the following conditions does not allow you to use the formula $\bar { x } \pm z _ { a / 2 } \sigma / \sqrt { n }$ to estimate $\mu$ ?

In determining the sample size n needed to estimate the population mean, n is higher if the population standard deviation $\sigma$ is higher.

A 99% confidence interval estimate of the population mean $\mu$ can be interpreted to mean:

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests Optional

Simple Linear Regression and Correlation

Multiple Regression

Filters

Exam 10: Introduction to Estimation

An unbiased estimator is a sample statistic whose expected value equals the population parameter.

Is the sample mean a consistent estimator of the population mean? Explain

Explain briefly why interval estimators are preferred to point estimators.

To estimate with 95% confidence the mean of a normal population whose standard deviation is assumed to be 4 and the maximum allowable sampling error is assumed to be 1, requires a random sample of size 62.

Because n is an integer and we want the bound on the error of estimation to be no more than a given amount, any non-integer value found for n must always be rounded ____________________.

Other things being equal, as the confidence level increases, the width of the confidence interval increases.

Statisticians can control the ____________________ of a confidence interval by determining the sample size necessary to produce the desired results.

How large a sample of federal employees in Nevada should be taken if we want to estimate with 98% confidence the mean salary to within $2,000. The population standard deviation is assumed to be $10,500.

The sample ____________________ is an unbiased estimator for the population mean.

An unbiased estimator of a population parameter is defined as:

In the formula xˉ±za/2σ/n\bar { x } \pm z _ { a / 2 } \sigma / \sqrt { n }xˉ±za/2​σ/n​ , the subscript α\alphaα / 2 refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

The term 1 - α\alphaα refers to:

Which of the following conditions does not allow you to use the formula xˉ±za/2σ/n\bar { x } \pm z _ { a / 2 } \sigma / \sqrt { n }xˉ±za/2​σ/n​ to estimate μ\muμ ?

In determining the sample size n needed to estimate the population mean, n is higher if the population standard deviation σ\sigmaσ is higher.

A 99% confidence interval estimate of the population mean μ\muμ can be interpreted to mean:

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests Optional

Simple Linear Regression and Correlation

Multiple Regression

Filters

In the formula $\bar { x } \pm z _ { a / 2 } \sigma / \sqrt { n }$ , the subscript $\alpha$ / 2 refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

The term 1 - $\alpha$ refers to:

Which of the following conditions does not allow you to use the formula $\bar { x } \pm z _ { a / 2 } \sigma / \sqrt { n }$ to estimate $\mu$ ?

In determining the sample size n needed to estimate the population mean, n is higher if the population standard deviation $\sigma$ is higher.

A 99% confidence interval estimate of the population mean $\mu$ can be interpreted to mean: