leiyou

 

3、Which of the following statements about sampling and estimation is most accurate?

A) A confidence interval estimate consists of a range of values that bracket the parameter with a specified level of probability, 1 ? β.

B) Time-series data are observations over individual units at a point in time.

C) Cross-sectional data are a set of values of a particular variable in sequential time periods.

D) A point estimate is a single estimate of an unknown population parameter calculated as a sample mean.

leiyou

 

The correct answer is Ｄ　

Time-series data are observations taken at specific and equally-spaced points.

Cross-sectional data are a sample of observations taken at a single point in time.

A confidence interval estimate consists of a range of values that bracket the parameter with a specified level of probability, 1 ? α.

leiyou

 

４、Which of the following would result in a wider confidence interval? A:

A) higher degree of confidence. 

B) higher alpha level. 

C) higher point estimate. 

D) greater level of significance. 

leiyou

 

The correct answer is A

A higher degree of confidence (e.g. 99% instead of 95%) would require a higher reliability factor (2.575 instead of 1.96 assuming a normal distribution). A wider confidence interval corresponds to a lower alpha significance level and the point estimate does not affect the width of the confidence interval.

leiyou

 

5、Which of the following statements regarding confidence intervals is most accurate?

A) The higher the alpha level, the wider the confidence interval.

B) The lower the alpha level, the wider the confidence interval. 

C) The relationship between the alpha level and the confidence interval cannot be ascertained. 

D) The lower the degree of confidence, the wider the confidence interval.

leiyou

 

The correct answer is B

A higher degree of confidence requires a wider confidence interval. The degree of confidence is equal to one minus the alpha level, and so the wider the confidence interval, the higher the degree of confidence and the lower the alpha level. Note that the lower alpha level requires a higher reliability factor which results in the wider confidence interval.

leiyou

 

AIM 7: Define and list the properties of point estimators and distinguish between unbiased and biased estimators.

1、The sample mean is an unbiased estimator of the population mean because the:

A) sampling distribution of the sample mean has the smallest variance of any other unbiased estimators of the population mean.

B) expected value of the sample mean is equal to the population mean.

C) sample mean provides a more accurate estimate of the population mean as the sample size increases.

D) sampling distribution of the sample mean is normal.

leiyou

 

The correct answer is B

An unbiased estimator is one for which the expected value of the estimator is equal to the parameter you are trying to estimate.

leiyou

 

AIM 8: Define an efficient estimator and consistent estimator.

1、The sample mean is a consistent estimator of the population mean because the:

A) expected value of the sample mean is equal to the population mean.

B) sampling distribution of the sample mean has the smallest variance of any other unbiased estimators of the population mean.

C) sample mean provides a more accurate estimate of the population mean as the sample size increases.

D) sampling distribution of the sample mean is normal.

leiyou

 

The correct answer is C

A consistent estimator provides a more accurate estimate of the parameter as the sample size increases.