Z statistic

In probability distribution chapter, the numerator of z statistic formula is x - xbar. But in hypothesis testing chapter the numerator is xbar - x. Why is this so?

Anyone?

Your assessment of the calculation in hypothesis testing is incorrect.

It’s not

xbar – x

It’s

sample mean − hypothesized mean

Thanks. But why did the mean change places ? Or are both the formulas unrelated?

It didn’t change places.

In both cases we’re subtracting a mean value from a statistic:

  • In the probability section, the statistic is a random value from a distribution, and the mean value is the mean of that distribution.
  • In the hypothesis testing section, the statistic is the mean value of a sample, and the mean value is the hypothesized mean value for the distribution from which that sample was taken.

Ah. Got it. Thanks a lot.

You’re quite welcome.