Sampling and Estimation

Question 1

Sampling error formula

Answer 1

sampling error of the mean = ^x - mue

ie sample mean - population mean

Question 2

Systematic sampling

Answer 2

• select every kth member of the population until we have a sample of the desired size
• divide the entire population by the desired sample size

Question 3

Stratified Random Sampling

Answer 3

• population is devided into subgroups based on one or more distinguishing characteristics.
• samples are then drawn from each subgroup, with their sample size proportional to the size of the subgroup relative to the population
• the sample will have the same distribution of key characteristics as the overall population
• more precise than simple random sampling

Question 4

Cluster sampling

Answer 4

• similar to stratified random sampling, but requires the population to be divided into subpopulations, called clusters
• each cluster is essentially a mini-representation of the entire population
• for voting districts or school districts, market surveys
• less accurate but more time and cost-efficient

Question 5

Standard error

Answer 5

SE = population (sample) stdv / sq root of n

Question 6

The three desirable properties of an estimator are:

Answer 6

• unbiasedness
• efficiency
• consistency

Question 7

Unbiasedness

Answer 7

• its expected value is equal to the parameter being estimated

Question 8

Efficiency

Answer 8

• has the lowest variance as compared to other unbiased estimators of the same parameter

Question 9

Consistency

Answer 9

• as sample size increases, the sampling error decreases and the estimates get closer to the actual value

Question 10

Z score and “reliability factor” for:
90% CI
95% CI
99% CI

Answer 10

Z “reliability factor”
90% CI .05 1.65
95% CI .025 1.96
99% CI .005 2.58

Question 11

Confidence Interval formula

Answer 11

CI = point estimate +- (reliability factor * std error)

point estimate ie mean

CI = ^x +- (Z a/2 * (pop std / sqrt n))

Z a/2: 1.65, 1.96, 2.58

CI = ^x +- (t a/2 * (sample std / sqrt n))

Question 12

Significance level:

Answer 12

a (alpha)

a = .1 =
90% CI, a/2 = .05, reliability factor z=.05 = 1.65

a = .05
95% CI, a/2 = .025, reliability factor z=.025 = 1.96

a = .01
99% CI, a/2 = .005, reliability factor z=.005 = 2.58

Question 13

Significance level:

Answer 13

a (alpha)

a = .1 =
90% CI, a/2 = .05, reliability factor z=.05 = 1.65

a = .05
95% CI, a/2 = .025, reliability factor z=.025 = 1.96

a = .01
99% CI, a/2 = .005, reliability factor z=.005 = 2.58

Question 14

Which distribution (z or t) is used for:
- For a normal distribution, variance is known,     n <30
- For a normal distribution, variance is known, 
n >= 30
- For a normal distribution, variance is unknown, n < 30
- For a normal distribution, variance is unknown, n >= 30

Answer 14

• For a normal distribution, variance is known, n <30
  z distribution
• For a normal distribution, variance is known,
  n >= 30
  z distribution
• For a normal distribution, variance is unknown, n < 30
  t distribution
• For a normal distribution, variance is unknown, n >= 30
  t or z distribution

Question 15

Which distribution (z or t) is used for:

• For a non-normal distribution, variance is known, n < 30
• For a non-normal distribution, variance is known, n >= 30
• For a non-normal distribution, variance is unknown, n < 30
• For a non-normal distribution, variance is known, n >= 30

Answer 15

• For a non-normal distribution, variance is known, n < 30
  NA
• For a non-normal distribution, variance is known, n >= 30
  z distribution
• For a non-normal distribution, variance is unknown, n < 30
  NA
• For a non-normal distribution, variance is known, n >= 30
  t or z distribution

Question 16

A larger sample size will…

Answer 16

• decrease the CI width and improves precision

Question 17

When sample size (n) increases…

Answer 17

• the standard error (s/squrt n) decreases

Question 18

Bootstrap

Answer 18

• treat the randomly drawn sample as if it were the actually the population
• take smaller samples from the larger sample one at a time and return them to the data, “sampling with replacement”
• the researcher has to decide how many repetitions are appropriate

Question 19

Jackknife

Answer 19

• start with a sample of data
• subsequent samples are created by leaving out one observation at a time from the set, no replacement
• for a sample size of n, jackknife usually requires n repetitions
• used to reduce the vias of an estimator
• will produce similar results with every run

Question 20

List the sampling biases

Answer 20

• data-snooping
• sample selection
• look-ahead
• time period

Question 21

Data-snooping Bias

Answer 21

• practice of analyzing the same data again and again, till a pattern that works is identified
• signs:
  too much digging/too little confidence
  no story/no future

Question 22

Sample Selection Bias

Answer 22

• survivorship bias

- backfill bias

Question 23

Look-ahead Bias

Answer 23

• if a test uses information that was not available to market participants at the time the market participants act in the model
• ie using year-end P/B values if the decision would have taken place in Q2 of that fiscal year

Question 24

Time-period Bias

Answer 24

• could use a time series that is too short, or too long