Question 1

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

Accepted Answer

Yes,the mean is consistent because it is unbiased and the standard error grows smaller as the sample size n increases.

Question 2

In developing an interval estimate for a population mean,the population standard deviation σ was assumed to be 10.The interval estimate was 50.92 ± 2.14.Had σ equaled 20,the interval estimate would be

Accepted Answer

A) 60.92 ± 2.14 
B) 50.92 ± 12.14 
C) 101.84 ± 4.28 
D) 50.92 ± 4.28 
A) 60.92 ± 2.14 
B) 50.92 ± 12.14 
C) 101.84 ± 4.28 
D) 50.92 ± 4.28 D

Question 3

The smallest number in a confidence interval is abbreviated by ____________________.

Accepted Answer

LCL

Question 4

A research firm has been contracted to estimate the mean weekly family expenditure on clothes.He believes that the standard deviation of the weekly expenditure is $125.Determine with 99% confidence the number of families that must be sampled to estimate the mean weekly family expenditure on clothes to within $15.

Accepted Answer

n = 463 (u

Question 5

Suppose a 95% confidence interval for μ turns out to be (1,000,2,100).What does it mean to be 95% confident?

Accepted Answer

A) In repeated sampling,the population parameter would fall in the resulting interval 95% of the time. 
B) 95% of the observations in the entire population fall in the given interval. 
C) 95% of the observations in the sample fall in the given interval. 
D) None of these choices. 
A) In repeated sampling,the population parameter would fall in the resulting interval 95% of the time. 
B) 95% of the observations in the entire population fall in the given interval. 
C) 95% of the observations in the sample fall in the given interval. 
D) None of these choices.

Question 6

A sample of 49 measurements of tensile strength for roof hangers are calculated to have a mean of 2.45 and a standard deviation of 0.25.(Units are Newton's per square meter.)
a.Determine the 95% confidence interval for mean tensile strength for all hangers.
b.Interpret this confidence interval.

Accepted Answer

a. LCL = 2.38 and UCL = 2.52 (Newton's p

Question 7

The larger the confidence level used in constructing a confidence interval estimate of the population mean,the narrower the confidence interval.

Accepted Answer

A) True 
 B)False

Question 8

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

Accepted Answer

A) True 
 B)False

Question 9

An estimator is said to be consistent if:

Accepted Answer

A) the difference between the estimator and the population parameter grows smaller as the sample size grows larger. 
B) it is an unbiased estimator. 
C) the variance of the estimator is zero. 
D) the difference between the estimator and the population parameter stays the same as the sample size grows larger. 
A) the difference between the estimator and the population parameter grows smaller as the sample size grows larger. 
B) it is an unbiased estimator. 
C) the variance of the estimator is zero. 
D) the difference between the estimator and the population parameter stays the same as the sample size grows larger.

Question 10

It is desired to estimate the average total compensation of CEOs in the publishing industry.Data were randomly collected from 18 CEOs and 95% confidence interval was calculated to be ($2,190,000,$4,720,000).Based on the interval above,do you believe the actual average total compensation of CEOs in the publishing industry could be $3,000,000?

Accepted Answer

A) Yes,and I am sure of that. 
B) Yes,and I am 95% confident of that. 
C) No,and I am sure of that. 
D) No,and I am 95% confident of that. 
A) Yes,and I am sure of that. 
B) Yes,and I am 95% confident of that. 
C) No,and I am sure of that. 
D) No,and I am 95% confident of that.

Question 11

If there are two unbiased estimators of a population parameter available,the one that has the smallest variance is said to be:

Accepted Answer

A) a biased estimator. 
B) relatively efficient. 
C) consistent. 
D) relatively unbiased. 
A) a biased estimator. 
B) relatively efficient. 
C) consistent. 
D) relatively unbiased.

Question 12

The sample variance (where you divide by n − 1)is an unbiased estimator of the population variance.

Accepted Answer

A) True 
 B)False

Question 13

The version of the sample variance where you divide by ____________________ gives you an unbiased estimator of the population variance.

Accepted Answer

The answer of The version of the sample variance where...

Question 14

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

Accepted Answer

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

Question 15

In determining the size n needed to estimate the population mean,n increases as the confidence level decreases.

Accepted Answer

A) True 
 B)False

Question 16

The lower limit of the 90% confidence interval for μ,where n = 64,   = 70,and σ = 20,is 65.89.

Accepted Answer

A) True 
 B)False

Question 17

Which of the following statements is false regarding the sample size needed to estimate a population mean?

Accepted Answer

A) It is directly proportional to the population variance. 
B) It is directly proportional to the square of zα / 2. 
C) It is directly proportional to the square of the maximum allowable error B. 
D) None of these choices. 
A) It is directly proportional to the population variance. 
B) It is directly proportional to the square of zα / 2. 
C) It is directly proportional to the square of the maximum allowable error B. 
D) None of these choices.

Question 18

Which of the following is an incorrect statement about a 90% confidence interval?

Accepted Answer

A) If we repeatedly draw samples of the same size from the same population,90% of the resulting confidence intervals will include μ. 
B) There is a 90% probability that the population mean μ will lie between the lower confidence limit (LCL)and the upper confidence limit (UCL). 
C) We are 90% confident that our sample mean equals the population mean μ. 
D) 90% of the population values will lie within the confidence interval. 
A) If we repeatedly draw samples of the same size from the same population,90% of the resulting confidence intervals will include μ. 
B) There is a 90% probability that the population mean μ will lie between the lower confidence limit (LCL)and the upper confidence limit (UCL). 
C) We are 90% confident that our sample mean equals the population mean μ. 
D) 90% of the population values will lie within the confidence interval.

Question 19

A 99% confidence interval estimate of the population mean μ 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.

Question 20

In thisChapter you need four values to construct the confidence interval estimate of μ.They are the sample mean,the sample size,the population standard deviation,and the confidence level.

Accepted Answer

A) True 
 B)False

Exam 10: Introduction to Estimation

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

In developing an interval estimate for a population mean,the population standard deviation σ was assumed to be 10.The interval estimate was 50.92 ± 2.14.Had σ equaled 20,the interval estimate would be

The smallest number in a confidence interval is abbreviated by ____________________.

Suppose a 95% confidence interval for μ turns out to be (1,000,2,100).What does it mean to be 95% confident?

A sample of 49 measurements of tensile strength for roof hangers are calculated to have a mean of 2.45 and a standard deviation of 0.25.(Units are Newton's per square meter.) a.Determine the 95% confidence interval for mean tensile strength for all hangers. b.Interpret this confidence interval.

The larger the confidence level used in constructing a confidence interval estimate of the population mean,the narrower the confidence interval.

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

An estimator is said to be consistent if:

If there are two unbiased estimators of a population parameter available,the one that has the smallest variance is said to be:

The sample variance (where you divide by n − 1)is an unbiased estimator of the population variance.

The version of the sample variance where you divide by ____________________ gives you an unbiased estimator of the population variance.

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

In determining the size n needed to estimate the population mean,n increases as the confidence level decreases.

The lower limit of the 90% confidence interval for μ,where n = 64, = 70,and σ = 20,is 65.89.

Which of the following statements is false regarding the sample size needed to estimate a population mean?

Which of the following is an incorrect statement about a 90% confidence interval?

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

In thisChapter you need four values to construct the confidence interval estimate of μ.They are the sample mean,the sample size,the population standard deviation,and the confidence level.

What Is Statistics

Graphical Descriptive Techniques 1

Graphical Descriptive Techniques 2

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

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Statistics

Time-Series Analytics and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

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