Question

Atlis 11 32 +233 D, The eccett B is the Men hauty eatnips oFAs is caal a 1 les Mon 30.dkMen lacre, is lgan kith、fesn Gte. 8, is the ditkee ia Mean hey ampedwoen une is calle

Answer 1

Solution:

We have the following regression model of average hourly earnings on age:

AHEi = 18.32 + 2.33*Di, where Di = 0 for age <= 30, and Di = 1 for age > 30

Denoting all betas by b, for ease of writing. So, the estimate of b1 = 2.33 (and that of b0 = 18.32)

We are required to test the hypothesis:

H0: b1 <= 0

H1: b1 > 0

Then, test statistic = (b1^ - b1)/s.e(b1^) (where s.e(b1^) is standard error of b1^)

Test statistic = (2.33 - 0)/0.2496 = 9.335

At 5% level of significance, critical value for such single tailed test is -1.645 (using z tables at z_0.05)

Since, |-1.645| < |9.335|, that is since critical value is less than test statistic in absolute terms, we can claim that null hypothesis is rejected. In other words, we reject that b1 <= 0, or do not reject that b1 > 0.

Conclusion: Workers with age greater than 30 indeed have a higher average hourly earnings than the younger group.