Sampling and Estimation

Question 1

What is simple random sampling?

Answer 1

A method of selecting a sample in such a way that each item or person in the population being studied has the same probability of being included in the sample.

Question 2

What is a sampling distribution?

Answer 2

The distribution of all values that a sample statistic can take on when computed from samples of identical size randomly drawn from the same population.

Question 3

What is sampling error?

Answer 3

1. The difference between a sample statistic and its corresponding population parameter.
2. Using sample data presents the risk that results found in an analysis do not represent the results that would be obtained from using data involving the entire population from which the sample was derived.

Question 4

What is stratified random sampling?

Answer 4

1. Involves randomly selecting samples proportionally from subgroups that are formed based on one or more distinguishing characteristics, so that the sample will have the same distribution of these characteristics as the overall population.
2. Ex: Stratification based on age groups of population

Question 5

What is time series data?

Answer 5

Time-series data consists of observations taken at specific and equally spaced points in time.

Question 6

What is cross sectional data?

Answer 6

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

Question 7

What is the central limit theorem?

Answer 7

States that for a population with a mean μ and a finite variance σ², the sampling distribution of the sample mean of all possible samples of size n (for n ≥ 30) will be approximately normally distributed with a mean equal to μ and a variance equal to σ² / n.

Question 8

What is the standard error of the sample mean?

Answer 8

The standard deviation of the distribution of the sample means.

Question 9

What is the calculation for the standard error of the sample mean, when the the population standard deviation is known?

Answer 9

where σ, the population standard deviation

Question 10

What is the calculation for the standard error of the sample mean, when the the population standard deviation is unknown?

Answer 10

Where s, the sample standard deviation, is used because the population standard deviation is unknown

Question 11

What are the three desirable properties of an estimator?

Answer 11

1. Unbiasedness (sign of estimation error is random),
2. Efficiency (lower sampling error than any other unbiased estimator), and
3. Consistency (variance of sampling error decreases with sample size).

Question 12

What is a point estimate?

Answer 12

1. Point estimates are single value estimates of population parameters.
2. Ex: the sample mean is essentially a point estimate of a population mean.

Question 13

What is an estimator?

Answer 13

1. An estimator is a formula used to compute a point estimate.

Question 14

What is a confidence interval?

Answer 14

Ranges of values, within which the actual value of the parameter will lie with a given probability.

Question 15

What is the calculation for the confidence interval?

Answer 15

confidence interval = point estimate ± (reliability factor × standard error)

Question 16

What is the reliability factor?

Answer 16

A number that depends on the sampling distribution of the point estimate and the probability that the point estimate falls in the confidence interval.

Question 17

Describe the properties of Student’s t-distribution:

Answer 17

1. Similar, but not identical, to the normal distribution in shape.
2. Defined by the degrees of freedom
3. Has fatter tails compared to the normal distribution.

Question 18

What is the calculation for Student’s t-distribution’s degress of freedom?

Answer 18

n − 1

Question 19

Does a greater or lesser degree of freedom(df) make the Student’s t-distribution more closely resemble a normal distribution?

Answer 19

1. Student’s t–distribution is closer to the normal distribution when df is greater.

Question 20

What effect does a greater degree of freedom have on the confidence interval in student’s t-distribution?

Answer 20

Confidence intervals are narrower when df is greater.

Question 21

For a normally distributed population, when can a z-statistic be used to construct a confidence interval for it’s mean?

Answer 21

1. When variance is known
2. Acceptable in the case of a normal population with an unknown variance if the sample size is large (30+).

Question 22

For a normally distributed population, when can a t-statistic be used to construct a confidence interval for it’s mean?

Answer 22

When the variance is unknown

Question 23

What effect does increasing sample size have on parameter estimates and confidence intervals?

Answer 23

1. Generally improve parameter estimates
2. Narrow confidence intervals.

Question 24

What are the five types of sampling method bias?

Answer 24

1. Data mining (significant relationships that have occurred by chance),
2. Sample selection bias (selection is non-random),
3. Look-ahead bias (basing the test at a point in time on data not available at that time),
4. Survivorship bias (using only surviving mutual funds, hedge funds, etc.), and
5. Time-period bias (the relation does not hold over other time periods).