(R10) Sampling and Estimation

Question 1

Define Simple Random Sampling and provide two methods

Answer 1

Each element has an equal probability of being chosen; 1) random number generate or 2) select every kth element

Question 2

Sampling Distribution

Answer 2

The distribution of all distinct possible values that a statistic can assume when computed from samples of the same size randomly drawn from the same population

Question 3

Sampling error

Answer 3

The difference between the observed value of a statistic and the quantity it is intended to estimate (Sample mean - population mean)

Question 4

Stratified Random Sampling

Answer 4

• Separate the population into smaller groups based on one more distinguishing characteristics; then use simple random sampling
• provides more precise mean and variance

Question 5

Three Data Types

Answer 5

1. Time Series
2. Cross-Sectional
3. Panel

Question 6

Time Series Data

Answer 6

Take a variable or multiple variables and observe how the variables change over a period of time
i.e. Monthly returns on Microsoft stock from Jan 1994 to Dec 2004.

Question 7

Cross-Sectional Data

Answer 7

Multiple observational units at a point in time

i.e Sales for 30 different companies for a particular quarter

Question 8

Longitudinal Data

Answer 8

Observations over time of multiple characteristics of the same entity, such as unemployment, inflation anf GDP growth rates, for a country over 10 years.

Question 9

Panel Data

Answer 9

Time series + cross sectional. Data that contains observations over time of the same characteristic for multiple entities, such as debt/equity ratios for 20 companies over 24 quarters.

Question 10

Standard Error Formula

Answer 10

Standard deviation divided by square root of n; the standard deviation of the distribution of the sample means.

Question 11

Central Limit Theorem

Answer 11

Theorem that states for simple random samples of size n, from a population with a mean u, and a finite variance, sigma^2, the sampling distribution of the sample mean, Xbar, approaches a normal probability distribution with mean u, and a variance equal to sigma^2 / N as the sample size becomes large.

Question 12

Properties of CLT

Answer 12

• If the sample size, n, is sufficiently large (n>= 30), the sampling distribution of the sample means will be approximately normal.
• • The mean of the population, u, and the mean of the distribution of all possible sample means are equal.
• **The variance of the distribution of sample means is sigma^2 /N. the population variance divided by the sample size.

Question 13

Desired Properties of an Estimator

Answer 13

1. Unbiasedness - when the expected value of the estimator is equal to the parameter you are trying to estimate.
2. Efficient – if the variance of its sampling distribution is smaller than all the other unbiased estimators of the parameter you are trying to estimate.
3. Consistent - the accuracy of the parameter estimate increases as the sample size increases.

Question 14

Point Estimates

Answer 14

Sample mean and sample variance are point estimates

Question 15

Confidence Interval Formula

Answer 15

Point estimate +/- reliability factor * standard error

C.I. = Xbar + z * (sigma / n^(1/2))

Question 16

Distribution with known variance, which table should be used to create confidence interval?

Answer 16

Use Z score

Question 17

Distribution with unknown variance, which table should be used to create confidence interval?

Answer 17

Use t score if sample is less than 30; use t or z score if sample is greater than 30

Question 18

Level of Significance

Answer 18

How confident your estimate is, denoted by alpha

Question 19

Characteristics of T-Distribution

Answer 19

1. Centered at Zero
2. Flatter than a normal distribution
3. As df increases, shape becomes more spiked and tails become thinner.
4. t-test levels of significance only correspond to one tail probabilities

Question 20

Confidence intervals are affected by:

Answer 20

• z score or t score
• alpha - level of confidence
• n - number of samples

Question 21

Data mining bias

Answer 21

Bias that refers to results where the statistical significance of the pattern is overestimated because the results were found through data-mining (the practice of hitting a data set over and over again until you hit gold)

Question 22

Sample selection bias

Answer 22

Bias which occurs when some data is systematically excluded from the analysis, usually because of the lack of availability (survivorship bias in mutual funds)

Question 23

Look ahead basis

Answer 23

Occurs when a study tests a relationship using sample data that was not available on the test date (i.e. stock price/returns vs. accounting data)

Question 24

Time period basis

Answer 24

Results only apply for that specific time period

Question 25

Unbiased estimator

Answer 25

When the expected value of the estimator is equal to the parameter you are trying to estimate.

Question 26

Efficient Estimator

Answer 26

If the variance of its sampling distribution is smaller than all the other unbiased estimators of the parameter you are trying to estimate.

Question 27

Consistent Estimator

Answer 27

The accuracy of the parameter estimate increases as the sample size increases.