Q1. Which of the following statements about sampling and estimation is most accurate?

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

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

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

Q2. 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 probability that a parameter lies within a range of estimated values is given by α.

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.

Q3. 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)   (1 − α) percent confidence interval.

B)   α percent confidence interval.

C)   α percent point estimate.

Q4. Which of the following characterizes the typical construction of a confidence interval correctly?

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

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

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

答案和详解如下：

Q1. Which of the following statements about sampling and estimation is most accurate?

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

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

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

Correct answer is A)

Time-series data are observations taken at specific and equally-spaced points.
A confidence interval estimate consists of a range of values that bracket the parameter with a specified level of probability, 1 − α.

Q2. 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 probability that a parameter lies within a range of estimated values is given by α.

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.

Correct answer is A)

The probability that a parameter lies within a range of estimated values is given by 1 − σ. The standard error of the sample means when the standard deviation of the population is known equals σ / √n, where σ = population standard deviation.

Q3. 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)   (1 − α) percent confidence interval.

B)   α percent confidence interval.

C)   α percent point estimate.

Correct answer is A)

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 percent point estimate or a (1 − α) percent cross-sectional point estimate.

Q4. Which of the following characterizes the typical construction of a confidence interval correctly?

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

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

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

Correct answer is 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

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