Sampling and Estimation

Question 1

Simple random sampling

Answer 1

Process of selecting sample where each member of population has equal chance of being selected

Question 2

Sampling distribution

Answer 2

Distribution of all distinct possible values that statistic can assume when computed from samples of same size drawn randomly from same population

Question 3

Simple random vs. stratified random sampling

Answer 3

Stratified involves dividing population into subpopulations based on certain criteria, then using simple random sampling in each stratum. Allows making sure that certain populations are represented in sample.

Question 4

Time series vs. cross sectional data

Answer 4

Sequence of information over intervals of time vs. data on some characteristic at set point in time

Question 5

Central limit theorem and its importance

Answer 5

Given population with mean μ and finite variance σ^2, sampling distribution of sample mean computed from samples of n size will be approximately normal with mean μ and variance of σ^2/n when sample size is greater than 30.

Allows making precise probability statements about POPULATION mean by using sample mean, regardless of distribution of population

Question 6

Calculate and interpret standard error of sample mean

Answer 6

standard deviation (pop or samp) / square root of n

It is the standard deviation of sampling distribution of sample mean.

Question 7

Desirable properties of estimator

Answer 7

Unbiased - expected value equals parameter intended to estimate

Efficient - no other unbiased estimator of same parameter has smaller variance of sampling distribution

Consistent - probability of estimates close to value of population parameter increases as sample size increases

Question 8

Point estimate vs. confidence interval estimate of population parameter

Answer 8

Point estimate - single number used to estimate parameter

Confidence interval estimate - range of values that brackets population parameter with probability 1 - α (degree of confidence) that it will contain the parameter [100(1-α)%]

Question 9

Describe properties of Student’s t-distribution

Answer 9

Symmetrical probability distribution defined by single parameter - degree of freedom

Can use to construct confidence intervals for population mean when population variance is UNKNOWN

Question 10

calculate and interpret degrees of freedom for t-distribution

Answer 10

n-1

Number of degrees of freedom in estimating population variance

Question 11

Calculate and interpret confidence interval for population mean with normal distribution and known population variance

Answer 11

sample mean +- z (sub α/2) * (σ/square root of n)

Question 12

Calculate and interpret confidence interval for population mean with normal distribution and unknown population variance

Answer 12

Only use if sample large or population normally distributed

sample mean +- t (sub α/2) * (s/square root of n)

Question 13

Calculate and interpret confidence interval for population mean with normal distribution and unknown variance and large sample size

Answer 13

Only use if sample large or population normally distributed

sample mean +- t (sub α/2) * (s/square root of n)

Question 14

Appropriate sample size

Answer 14

Look at need for precision, risk of sampling from more than one population, expenses of different sample sizes

Question 15

Data mining bias

Answer 15

Errors arising from misuse of data. Drilling until finding something that works. Frequently these will fail in future because they are after-the-fact.

Watch for:

Too much digging, too little confidence
No story, no future

Question 16

Sample selection bias

Answer 16

Data availability leads to certain assets being excluded from analysis

Question 17

Survivorship bias

Answer 17

Funds, companies etc. no longer appear in sample because they went out of business

Question 18

Look-ahead bias

Answer 18

Using information not available on test date (e.g. looking at 12/31 price in light of year-end numbers that are not available on 12/31)

Question 19

Time-period bias

Answer 19

Using time period that may make results time-period specific

Question 20

Reliability factors for confidence intervals in t and z tests

Answer 20

Use correct column in tables for reliability factor:

90% - .05
95% - .025
99% - .005

More confidence you want, the less accurate you can be