Quantitative Methods V

Question 1

Null hypothesis

Answer 1

One you want to reject in order to assume alternate is correct

Question 2

Test statistic

same for Z and T

Answer 2

(sample mean - hypothesized mean) / standard error

remember, standard error = stdev / sqrt(n)

Question 3

Two tailed vs. one-tailed

Answer 3

Two tailed is Ho = something

One-tailed is Ho > something

Question 4

Type I error

Answer 4

Rejection of null when it’s actually true

Question 5

Type II error

Answer 5

Failure to reject when it is actually false

Question 6

Power of test

Answer 6

1 - probability of type II error

Question 7

Confidence interval (Z-test)

Answer 7

Sample mean - (standard error * critical z-value) < mean < sample mean + (standard error * critical z-value)

Question 8

P-value

Answer 8

Prob of test stat that would lead to a type I error.

Question 9

T-Test

Answer 9

Use if population variance is unknown and either:

1. Sample is large
2. Sample is small, but distribution is normal

Question 10

Z-Test

Answer 10

Use if population is normal, with known variance or when sample is large and population variance is unknown

Question 11

Sample distribution

Answer 11

Sample statistics computed from samples of the same size drawn from the same population

Question 12

Desired properties of estimators (3)

Answer 12

Efficiency, consistency and unbiasedness

Question 13

Data mining

Answer 13

Searching for trading patterns until one “works”

Question 14

Sample selection bias

Answer 14

Some data is systematically excluded (e.g. from lack of availability)

Question 15

Look ahead bias

Answer 15

Study tests relationship using sample data that wasn’t available on test date

Question 16

Time period bias

Answer 16

Either too long or too short

Question 17

Chi-squared (X^2)

Answer 17

Used for tests concerning variance of normally distributed population vs. sample

Symmetrical, approaches normal as d.f. increases

Chi is bounded by 0 so test stats can’t be negative

Question 18

Chi-squared test statistic

Answer 18

[(n-1) * sample variance] / hypothesized pop. variance

FYI, critical value is for one tail, so you have to adjust for two

Question 19

F-test

Answer 19

Tests equality of variances of two populations via samples of said populations

Populations are normal and samples are INDEPENDENT.

Bounded by 0 (like chi square)

Question 20

F-test: two tailed vs. one-tailed

Answer 20

Two tailed: variance of pop. 1 = variance pop. 2

One-tailed: variance of pop. 1 >= variance pop. 2

Question 21

F-statistic

Answer 21

Variance sample 1 / variance sample 2

Note: always put larger variance in numerator, use d.f. of larger sample and look at right tail.

Question 22

Difference in means test

Answer 22

T-statistic

Two INDEPENDENT samples, normally distributed populations

Formula won’t be on test.

Question 23

Paired comparisons test

Answer 23

T-test statistic

Used when samples are dependent.

Sample data must be normally distributed.

Question 24

Paired comparisons test (formula)

Answer 24

Tstat = (sample mean difference - mean) / standard error of mean difference

Sample mean difference = 1/n * sum(mean1 - mean2…)

Standard error = sample stdev / sqrt(n)

Question 25

Elliot wave theory - impulse wave

Answer 25

Direction of the prevailing trend, has five smaller waves

Question 26

Elliot wave theory - corrective wave

Answer 26

Against the prevailing trend, has three smaller waves.

Question 27

Type II Error probability

Answer 27

Calculate probability that you fail to reject the null when is actually false. Here you use the actual M and get the stat of (X-bar - M) / standard error.

Question 28

Treynor Ratio

Answer 28

(portfolio return - risk free return) / Beta

Question 29

Consistent estimator

Answer 29

Gets closer to population as n increases

Question 30

Unbiased estimator

Answer 30

Expected value = true population value

Question 31

Efficient estimator

Answer 31

Has a variance of sampling distributions that is lower than that of any other estimator