EXAMPLE $15\mathrm{.}3$ Studying job satisfaction

Does the job satisfaction of assembly workers differ when their work is machine$-$paced rather than self$-$paced? Assign workers either to an assembly line moving at a fixed pace or to a self$-$paced setting. All subjects work in both settings, in random order. This his ${?}_{i_a}$ matched pairs design. After two weeks in each work setting, the workers take a test of job satisfaction. The response variable is the difference in satisfaction scores, self$-$paced minus machine$-$paced.

The parameter of interest is the mean $$ of the differences in scores in the population of all assembly workers. The null hypothesis says that there is no difference between self. paced and machine$-$paced work, that is$,$

$H_0$:$=0$

The authors of the study wanted to know if the two work conditions have different levels of job satisfaction. They did not specify the direction of the difference. The alternative hypothesis is therefore two$-$sided:

$H_a$:$0$

The hypotheses should express the hopes or suspicions we have before we see the data. It is cheating to first look at the data and then frame hypotheses to fit what the data show. Thus, the fact that the workers in the study of Example $15\mathrm{.}3$ were more satisfed with self$-$paced work should not influence our choice of $H_a.$ If you do not havea specific direction firmly in mind in advance, use a two$-$sided alternative.