M8 -

Question 1

Whats correlation?

Answer 1

The association between two quantitative variables.

perfect positive correlation = 1
no correlation = 0

Question 2

Cenral limit Theorem

• def
• implication

Answer 2

• The distribution of mean values of samples of the size N that were drwan from the population converges with increasing N towards a normal distribution
• For samples of a size of above N =30, probabilities can be quantifies as estimates of the mean

Question 3

Estimates of the mean - sigma

Answer 3

• with a probability of 68% the mean of a random sample is in the range
  müh +-sigma
  (müh - mean value in the population, sigma = standard error of the sample mean)
• with a probability of 95,5% the mean of the sample is in the range of
  2müh +-sigma

Question 4

Standardization
-when is it standardized?
-

Answer 4

• a random varable is called standardized when its expected value is 0 and its variance is 1.
• define a new random variable Sn=x1+x2+xn
• expected value of Sn: mühn; variance ns²

Question 5

Hypotheses

• def
• criteria for sctientific hypotheses

Answer 5

• are assumptions about structral properties among phenomena
  they point beyond an individual situationa nd can be disproved by empirical data
• general validity
• falsifiable
• phrased as conditional clause/ equality/inequality

Question 6

general validity

Answer 6

is the extent to which a concept, conclusion or measurement is well-founded and corresponds accurately to the real world.

universal proposition / generalizable

Question 7

falsifable

Answer 7

it must be possible to imagine events that are in conflict with conditional clauses

Question 8

Null hypothesis

Alternative hypothesis

Answer 8

H0 contains the statement to be disproved
–> typically claims “there is no difference / effect” –> a statement that can be falsified by finding a significant difference

H1 claims the opposite
–> typically “there is a difference/effect” –> cannot be falsifed since a non-finding of a difference may be due to the fact that the difference was too small

Question 9

z-test

• def
• distribution of z
• what if p-value is less than the given level of sign

Answer 9

compare sample mean with pop mean

z-test: tells us whether the bcoeff for that IV is sign different from zero

• -> if b is different from zero, then this IV is making a sign contribution to the prediction of the outcome.
• normally distributed
• for N > 30
• KNOWN SD
• z is normally distributed
• p-value is less than the given level of sign., H0 must therefore be rejected

Question 10

one-tailed hypothesis

two-tailed hypothesis

Answer 10

• H1 unequal 10; its either smaller or bigger, may be both

- H1 avg > 20; its bigger but not smaller

Question 11

difference one and two-tailed tests
- p-value
z-value

Answer 11

ONE: compares the sample mean with the pop mean
TWO: compares 2 (in)dependent samples

• with equal z-values the critical p-value of the on-sd-t. is half as large as the one of the two-s-t.
• with equal p-values, the critial z-value o the one-s-t is less than the one of the two-s-t

Question 12

t-test

• purpose?
• p-value

Answer 12

ONE: compares sample mean with pop mean
TWO: compares (in)dependent samples

• for N < 30
• varibles normally distributed
• almot similar variation
• UNKOWN SD!
• p-value states at which significance level we can reject the null hypothesis

t-test: know how well the model fits the data and the contribution of individual predictors
–> linear regression