leiyou

 

The correct answer is A

Because we know the population standard deviation, we use the z-statistic. A 95% confidence level is constructed by taking the population mean and adding and subtracting the product of the z-statistic reliability (zα/2) factor times the known standard deviation of the population divided by the square root of the sample size: x ± zα/2 × ( σ / n1/2) = 60 ± (1.96) × (16 / 751/2) = 60 ± (1.96) × (16 / 8.6603) = 60 ± (1.96) × (1.85).

leiyou

 

3、The approximate 99% confidence interval for the population mean based on a sample of 60 returns with a mean of 7% and a sample standard deviation of 25% is closest to:

A) 1.584% to 14.584%.

B) -1.584% to 15.584%.

C) 0.546% to 13.454%.

D) 1.546% to 13.454%.

leiyou

 

The correct answer is B

The standard error for the mean = s / (n)0.5 = 25% / (60)0.5 = 3.227%. The critical value from the t-table should be based on 60 ? 1 = 59 df. Since the standard tables do not provide the critical value for 59 df the closest available value is for 60 df. This leaves us with an approximate confidence interval. Based on 99% confidence and df = 60, the critical t-value is 2.660. Therefore the 99% confidence interval is approximately: 7% ± 2.660(3.227) or 7% ± 8.584% or -1.584% to 15.584%.

If you use a z-statistic, the confidence interval is 7% ± 2.58(3.227) = -1.326% to 15.326%, which is closest to the correct choice.

leiyou

 

4、A nursery sells trees of different types and heights. Suppose that 75 pine trees are sold for planting at City Hall. These 75 trees average 60 inches in height with a standard deviation of 16 inches.

Using this information, construct a 95% confidence interval for the mean height of all trees in the nursery.

A) 60 + 1.96(1.85).

B) 60 + 1.96(16).

C) 0.8 + 1.96(16).

D) 0.8 + 1.96(1.85).

leiyou

 

The correct answer is A

The population standard deviation is the square root of the variance (√0.49 = 0.7). Because we know the population standard deviation, we use the z-statistic. The z-statistic reliability factor for a 95% confidence interval is 1.960. The confidence interval is $1.00 ± 1.960($0.7 / √36) or $1.00 ± $0.2287.

leiyou

 

2、A sample of size 25 is selected from a normal population. This sample has a mean of 15 and the population variance is 4.

Using this information, construct a 95% confidence interval for the population mean, m.

A) 15 ± 1.96(0.4).

B) 15 ± 1.96(2).

C) 15 ± 1.96(0.8).

D) 15 ± 1.96(4).

leiyou

 

The correct answer is A

Because we can compute the population standard deviation, we use the z-statistic.  A 95% confidence level is constructed by taking the population mean and adding and subtracting the product of the z-statistic reliability (zα/2) factor times the known standard deviation of the population divided by the square root of the sample size (note that the population variance is given and its positive square root is the standard deviation of the population): x ± zα/2 × ( σ / n1/2) = 15 ± 1.96 × (41/2 / 251/2) = 15 ± 1.96 × (0.4).

leiyou

 

3、If Estimator A is a more efficient estimator than Estimator B, it will have:

A) a smaller mean and the same variance. 

B) the same mean and a smaller variance. 

C) a smaller mean and a larger variance. 

D) the same mean and a larger variance.

leiyou

 

The correct answer is B

The more efficient estimator is the one that has the smaller variance, given that they both have the same mean.

leiyou

 

AIM 9: Define Best Linear Unbiased Estimator.

1、Shawn Choate is thinking about his graduate thesis. Still in the preliminary stage, he wants to choose a variable of study that has the most desirable statistical properties. The statistic he is presently considering has the following characteristics:

?            The expected value of the sample mean is equal to the population mean.

?            The variance of the sampling distribution is smaller than that for other estimators of the parameter.

?            As the sample size increases, the standard error of the sample mean rises and the sampling distribution is centered more closely on the mean.

?            Select the best choice. Choate’s estimator is:

A) unbiased, efficient, and consistent.

B) efficient and consistent.

C) unbiased and consistent.

D) unbiased and efficient.