Question

An economic historian decides to study the heights of army recruits in Britain before 1820 and after 1820. In his regression, the main variable of interest (the dependent variable) is heights (measured in centimeters). He uses a series of dummy variables to capture socio-economic conditions via the occupations reported by the recruits. Setting “craftsmen” as the reference category, he reports the following coefficients and standard errors (the sample size is reported at the bottom of the table):

Variable	Coefficient	Standard Error
Constant	168.99	0.523
Craftsmen	Reference Category	-
Dummy for agricultural worker	1.64	0.301
Dummy for building worker	0.60	0.214
Dummy for dealing worker	0.58	0.433
Dummy for domestic servant	-0.84	0.376
Dummy for day labourers	0.02	0.146
Dummy for mining workers	0.75	0.335
Dummy for service worker	1.83	0.619
Dummy for transport worker	-0.88	0.805
Dummy for “other”	1.25	0.401
Dummy for “no occupation”	-2.49	0.639
Number of observations	15,740

Among the choices below, which statement correctly represents the height difference between domestic servants and building workers and also correctly depicts whether or not the variable for building workers is significant

1. Domestic servants are 0.24 cm shorter than building workers and the coefficient for building workers is not statistically significant
2. Domestic servants are 1.44 cm shorter than building workers and the coefficient for building workers is statistically significant at the 95% level
3. Domestic servants are 0.24 cm shorter than building workers and the coefficient for building workers is statistically significant at the 95% level
4. Domestic servants are 1.44 cm shorter than building workers and the coefficient for building workers is not statistically significant
5. None of the above

Answer 1

(b) Domestic servants are 1.44 cm shorter than building workers and the coefficient for building workers is statistically significant at the 95% level

The comparison between domestic servants and building workers can be made by finding out a difference between the the coefficient value of both. Thus, a difference between the two shows that domestic servants are 1.44 cm (-0.84 - 0.58) shorter than the building workers. Also the coefficient value is significant at 95% level when the coefficient value is less than the p-value of 95% confidence internval, which is 1.96. Since, coefficient value (0.6) is less than the p-value of 95% level, the building workers is statistically significant at the 95% level.