Sampling And Estimation

Question 1

A method of soliciting a sample in such a way that each item or person in the population being studied has the same likelihood of being in the sample

Answer 1

Simple Random Sampling

Question 2

The difference between a sample statistic and its corresponding population parameter

Answer 2

Sample Error

Question 3

A technique that uses a classification system to separate the population into smaller groups based on one or more distinguishing characteristics

Answer 3

Stratified Random Sampling

i.e. bond indexing

Question 4

Data which consists of observations taken over a period of time at a specific and equally spaced time interval.
i.e. Time - Series – set of monthly returns on Microsoft stock from Jan 1994 to Dec 2004.

Answer 4

Time Series Data

Question 5

Data that are a sample of observation taken at a single point in time.
i.e. Reported earnings per share of all NASDAQ companies as of Dec. 31, 2014.

Answer 5

Cross Sectional Data

Question 6

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

Answer 6

Longitudinal Data

Question 7

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

Answer 7

Panel Data

Question 8

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.

Answer 8

Central Limit Theorem

Question 9

Properties of CLT

Answer 9

• 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 10

Sample Error of Standard Mean Calculation

Answer 10

sigmaXbar = sigma / n^(1/2)

* the standard deviation of the distribution of the sample means.

Question 11

Desired Properties of an Estimator

Answer 11

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 12

Single (sample) values used to estimate a population parameter.

Answer 12

Point estimates

Question 13

A bell-shaped probability distribution that is symmetrical about its mean.

Answer 13

t-distribution
*Use t-distribution when constructing confidence intervals based on small samples (n <30) from populations with unknown variance and a normal distribution

Question 14

t-distributions have the following properties

Answer 14

1. Symmetrical
2. Has 1 parameter : Degrees of Freedom
3. Has more probability in the tails than the normal distribution
4. As df increases, the shape of the t-distribution more closely approaches a standard normal distribution

Question 15

The number of sample observations minus 1, for sample means

Answer 15

Degrees of Freedom (df)

Question 16

Characteristics of T-Distribution

Answer 16

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 17

This estimates result in a range of values within which the actual value of a parameter will lie, given the probability of 1-alpha

Answer 17

Confidence Intervals

Question 18

How confident your estimate is, denoted by alpha

Answer 18

Level of Significance

Question 19

Confidence Interval Calculation

Answer 19

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

Question 20

Distribution with known variance

Answer 20

Use z score

Question 21

Distribution with unknown variance

Answer 21

Use t score

Question 22

2 Limitations of “larger is better”

Answer 22

1. may contain observations from a different population

2. Cost

Question 23

Bias that refers to results where the statistical significance of the pattern is overestimated because the results were found through data-mining.

Answer 23

Data mining Bias

Question 24

Bias which occurs when some data is systematically excluded from the analysis, usually because of the lack of availability

Answer 24

Sample Selection Bias

*Survivorship bias in mutual funds

Question 25

Occurs when a study tests a relationship using sample data that was not available on the test date.

Answer 25

Look-ahead bias

Question 26

Results if the time period over which the data is gathered is either too short or too long.

Answer 26

Time-period Bias