Question

Reply to the following Discussion Question with a substantive post - one that demonstrates that you understand the mathematical concepts and provides an explanation rather than just making a simple statement about the topic. The z-statistic is calculated with the formula z = (sample statistic - null parameter)/(standard error). Why do we subtract the null parameter from the sample statistic? In other words, what does subtracting achieve for us? Why do we then divide that value by the standard error? *Answering "because that is what the formula says" will not be accepted. You need to get at the meaning of the z score by answering "why" we do these processes.

Answer 1

Substracting the null parameter from the sample statistic will re-locate the statistic to 0 i.e. the origin. The null parameter is the location parameter, substracting which from the sample statistic will translate the graph.

Again, dividing the value by standard error will re-scale the sample statistic. The standard error is the scale parameter, dividing the sample statistic by it will compress the pdf.

So, both these aspects are taken care of while standardizing the sample statistic.