4. [15 Marks] Data are collected on 3000 workers, their wages, ages and genders.

Question

4. [15 Marks] Data are collected on 3000 workers, their wages, ages and genders. The unit of wage is measured in thousands of pounds and the workers ages are measured in years. The gender equals 1 if the worker is male. Wages are regressed on age, age square (denoted as age sq in the regression) and gender. The results can be seen listed in the table below . reg wage age_ sq age gender Source Ss df MS = 3,000 -187.25 0.0000 = 0.1579 Adj R-squared = 0.1571 = 38.312 Number of obs F (3, 2996) Model 824541.261 3 274847.087 ProbF Residual 4397544.45 2,996 1467.80522 R-squared Total 5222085.71 2,999 1741.27566 Root MSE wage Coef. Std. Err. (95% Conf., Interval] 0392763 5.463365 0042582 .0559749 11.18 0.000 4.730172 .3739337 12.65 0.000 age sa 0476256 age 3.99698 gender23,15548 1.409948 16.42 0.000 20.39092 25.92005 cons #8.388705 7.846589-1.07 0.285-23.77395 6.996542

Explanation / Answer

(b) Here H0: 2= $ 25000

Ha : 2 $ 25000

Where 2is the regression or partial slope coefficient of gender in regression with wages.

Here sample 2= 23.15548

Standard error of the 2(s2) = 1.409948

Test statistic

t = (25 - 23.15548)/ 1.409948 = 1.3082

Here critical value of t for alpha = 0.05 and dF = 2996

tcritical= t0.05,2996 = 1.9608

so here t > tcriticalso we shall not reject the null hypothesis and can conclude that female workers earn 25 thousands pounds less than male workers.

Here we can calculate it with calculating 95% confidence interval for 2which is given as

95% confidence interval = (20.39092, 25.92005) that interval encompasses the value of 25 so, we shall not reject the null hypothesis and conclude that  female workers earn 25 thousands pounds less than male workers.

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