1.Which of the following statements about sampling and estimation is most accurate?

A)   The standard error of the sample means when the standard deviation of the population is unknown equals s / √n, where s = sample standard deviation.

B)   The standard deviation of the distribution of the sample means is the standard error of the residual.

C)   The standard error of the sample means when the standard deviation of the population is known equals σ / √n, where σ = sample standard deviation adjusted by n-1.

D)   The probability that a parameter lies within a range of estimated values is given by α.

2.Which of the following statements about sampling and estimation is TRUE?

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.

3.Which of the following characterizes the typical construction of a confidence interval correctly?

A)   Point estimate +/- (Standard error / Reliability factor).

B)   Point estimate +/- (Reliability factor x Standard error).

C)   (Reliability factor x Standard error) +/- Point estimate.

D)   Standard error +/- (Point estimate / Reliability factor).

4.A range of estimated values within which the actual value of a population parameter will lie with a given probability of 1 – α is a(n):

A)   α percent point estimate.

B)   α percent confidence interval.

C)   (1 - α) percent cross-sectional point estimate.

D)   (1 - α) percent confidence interval.

答案和详解如下：

1.Which of the following statements about sampling and estimation is most accurate?

A)   The standard error of the sample means when the standard deviation of the population is unknown equals s / √n, where s = sample standard deviation.

B)   The standard deviation of the distribution of the sample means is the standard error of the residual.

C)   The standard error of the sample means when the standard deviation of the population is known equals σ / √n, where σ = sample standard deviation adjusted by n-1.

D)   The probability that a parameter lies within a range of estimated values is given by α.

The correct answer was A)

This definition is correct. The other choices are false. The probability that a parameter lies within a range of estimated values is given by 1 - σ. The standard deviation of the distribution of the sample means is the standard error of the sample mean. The term residual is used during the discussion of regression that occurs later in this study session. The standard error of the sample means when the standard deviation of the population is known equals σ / √n, where σ = population standard deviation.

2.Which of the following statements about sampling and estimation is TRUE?

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.

The correct answer was 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.

3.Which of the following characterizes the typical construction of a confidence interval correctly?

A)   Point estimate +/- (Standard error / Reliability factor).

B)   Point estimate +/- (Reliability factor x Standard error).

C)   (Reliability factor x Standard error) +/- Point estimate.

D)   Standard error +/- (Point estimate / Reliability factor).

The correct answer was B)

We can construct a confidence interval by adding and subtracting some amount from the point estimate. In general, confidence intervals have the following form:
Point estimate +/- Reliability factor x Standard error
Point estimate = the value of a sample statistic of the population parameter
Reliability factor = a number that depends on the sampling distribution of the point estimate and the probability the point estimate falls in the confidence interval (1 – α)
Standard error = the standard error of the point estimate

4.A range of estimated values within which the actual value of a population parameter will lie with a given probability of 1 – α is a(n):

A)   α percent point estimate.

B)   α percent confidence interval.

C)   (1 - α) percent cross-sectional point estimate.

D)   (1 - α) percent confidence interval.

The correct answer was D)    

A 95% confidence interval for the population mean (α = 5% is the p-value), for example, is a range of estimates within which the actual value of the population mean will lie with a probability of 95%. Point estimates, on the other hand, are single (sample) values used to estimate population parameters. There is no such thing as a α% point estimate or a (1 - α)% cross-sectional point estimate.