leiyou

 

The correct answer is D

The estimator is unbiased because the expected value of the sample mean is equal to the population mean. The estimator is efficient because the variance of the sampling distribution is smaller than that for other estimators of the parameter.

The estimator is not consistent. To be consistent, as the sample size increases, the standard error of the sample mean should fall and the sampling distribution will be centered more closely on the mean. A consistent estimator provides a more accurate estimate of the parameter as the sample size increases.

leiyou

 

AIM 5: Define, calculate and interpret confidence interval, confidence coefficient, upper limit, lower limit, random interval.

1、The average U.S. dollar/Euro exchange rate from a sample of 36 monthly observations is $1.00/Euro. The population variance is 0.49. What is the 95% confidence interval for the mean U.S. dollar/Euro exchange rate?

A) $0.7713 to $1.2287.

B) $0.5100 to $1.4900.

C) $0.8075 to $1.1925.

D) $0.8657 to $1.1343.

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.

leiyou

 

2、If the variance of the sampling distribution of an estimator is smaller than all other unbiased estimators of the parameter of interest, the estimator is:

A) efficient.

B) reliable.

C) unbiased.

D) consistent.

leiyou

 

The correct answer is A

By definition.

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.