Clear and load dataset

clear
use "C:\Econ 107\LAB0\Stata dataset\cps92_08.dta"

(a) sample mean and confident interval

ttest ahe, by(year)

Results:

. ttest ahe, by(year)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
    1992 |   7,605    11.62637    .0643675    5.613272    11.50019    11.75254
    2008 |   7,711    18.97609    .1154672    10.13944    18.74975    19.20244
---------+--------------------------------------------------------------------
combined |  15,316    15.32666    .0726803    8.994762     15.1842    15.46912
---------+--------------------------------------------------------------------
    diff |           -7.349727    .1326828               -7.609801   -7.089653
------------------------------------------------------------------------------
    diff = mean(1992) - mean(2008)                                t = -55.3932
Ho: diff = 0                                     degrees of freedom =    15314

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 1.0000

(b) adjust the data

gen ahe92_08=ahe
replace ahe92_08=ahe92_08*215.2/140.3 if year==1992

ttest ahe92_08, by(year)

Results:

. gen ahe92_08=ahe

. 
. replace ahe92_08=ahe92_08*215.2/140.3 if year==1992
(7,605 real changes made)

. 
. 
. 
. ttest ahe92_08, by(year)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
    1992 |   7,605    17.83317    .0987304    8.609951    17.63963    18.02671
    2008 |   7,711    18.97609    .1154672    10.13944    18.74975    19.20244
---------+--------------------------------------------------------------------
combined |  15,316    18.40859    .0761822    9.428138    18.25926    18.55791
---------+--------------------------------------------------------------------
    diff |           -1.142922    .1520928               -1.441042   -.8448022
------------------------------------------------------------------------------
    diff = mean(1992) - mean(2008)                                t =  -7.5146
Ho: diff = 0                                     degrees of freedom =    15314

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 1.0000

(c)

We should use result in (b) since it is reasonable that we compare two wages in same price level.

(d) Bachelor degree 2008

ttest ahe if year == 2008, by(bachelor)

Results:

. ttest ahe if year == 2008, by(bachelor)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |   4,002    15.33174     .121733    7.700994    15.09308    15.57041
       1 |   3,709    22.90834     .179853    10.95333    22.55572    23.26096
---------+--------------------------------------------------------------------
combined |   7,711    18.97609    .1154672    10.13944    18.74975    19.20244
---------+--------------------------------------------------------------------
    diff |           -7.576594    .2144021               -7.996881   -7.156308
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t = -35.3382
Ho: diff = 0                                     degrees of freedom =     7709

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 1.0000

(e) Bachelor degree 1992

ttest ahe92_08 if year == 1992, by(bachelor)

Results:

. ttest ahe92_08 if year == 1992, by(bachelor)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |   4,643    15.31326    .1034966    7.052216    15.11036    15.51616
       1 |   2,962    21.78319    .1712247     9.31878    21.44745    22.11892
---------+--------------------------------------------------------------------
combined |   7,605    17.83317    .0987304    8.609951    17.63963    18.02671
---------+--------------------------------------------------------------------
    diff |           -6.469927    .1883968               -6.839237   -6.100617
------------------------------------------------------------------------------
    diff = mean(0) - mean(1)                                      t = -34.3420
Ho: diff = 0                                     degrees of freedom =     7603

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 1.0000

(f)

High school: 15.33174 -> 15.31326 decrease

College: 22.90834 -> 21.78319 decrease

Difference (absolute value): 6.469927 -> 7.576594 incease