Summary Statistics 2 for Economics

Lecture 1A
One population: mean μ when σ is known
1) Conditions and assumptions
- Random sample
- Quantitative data
- Population normal or n ≥ 30
2) Hypotheses
- H0: μ = …
- H1: μ ≠ …
3) Test statistics and its distribution
4) Rejection region
- Z ≥ Zcrit or Z ≤ -Zcrit
5) Sample outcome
6) Confrontation and decision
7) Conclusion
- Given the significant level of 5%, there is insufficient evidence to
infer that the mean age of the population in the Netherlands is higher
than 44 years

One population: mean μ when σ is unknown
1) Conditions and assumptions
- Random sample
- Quantitative data
- Population normal or n ≥ 30
- Population variance is unknown
2) Hypotheses
- H0: μ = …
- H1: μ ≠ …
4) Rejection region
T ≥ Tcrit or T ≤ -Tcrit

Matched pairs
- Comparing two groups of the same population
- E.g. before-after
(Independent samples compares two samples of two populations)

Two populations: matched pairs
1) Conditions and assumptions
- Random sample of matched pairs
- Quantitative data
- Population normal or n ≥ 30
- Population variance is unknown
2) Hypotheses
- H0: μD = …

, - H1: μD ≠ …
4) Rejection region
- T ≥ Tcrit or T ≤ -Tcrit

One population: variance (chi-square)
1) Conditions and assumptions
- Random sample
- Quantitative data
- Population normally distributed
2) Hypotheses
- H0: σ2 = …
- H1: σ2 ≠ …
4) Rejection region
- Upper region: Xobs ≥ Xcrit
- Lower region: Xcrit = X1-alpha -> Xobs ≤ Xcrit

Lecture 1B
Comparing two means
1) Conditions and assumptions
- Independent, random samples
- Quantitative data
- Population normal or n ≥ 30
2) Hypotheses
- H0: μ1 – μ2 = 0
- H1: μ1 – μ2 ≠ 0
4) Rejection region
- Z ≥ Zcrit or Z ≤ -Zcrit OR T ≥ Tcrit or T ≤ -Tcrit

Experiment design
- Matched pairs eliminates (or reduces) the effect of interfering factors
- Experimental
- With human intervention, researcher manipulates one or more
variables in order to study the effect on others
- Matched pairs
- Often expensive, takes long time or impossible
- Observational
- Merely observations, without human intervention
- Independent sample
- Interpretation of results often unclear



Comparing two variances
1) Conditions and assumptions
- Independent, random samples

, - Quantitative data
- Population normal or n ≥ 30
2) Hypotheses

- H0:

- H1:
4) Rejection region


- Critical value on the left side:

Lecture 2A




Levels of measurement
- Nominal (yes/no, merken, steden, geslacht etc.) -> has no order
- Ordinal (opinions, places in a race, verbal exam grade, feelings) ->
differences between options are not equal
-> These can both be coded with numbers, but are not quantitative

One population: proportion
1) Conditions and assumptions
- Random sample
- Nominal data
-nxp≥5
- n x (1-p) ≥ 5
2) Hypotheses
-