The other possibility is that there is, indeed, something going on.

In other words, promotion and gender are dependent, there is gender discrimination.

Observed difference in proportions, that's the proportions of promotions

between males and females, is not due to chance.

That is what we call our alternative hypothesis.

So how did we finally make the decision?

Remember that we actually did a simulation based

inference where we simulated the experiment under

the assumption of the null hypothesis being true.

In other words, under the assumption of independence.

In other words, leaving everything up to chance.

And at each simulation, we calculated the difference between the

proportion of promotions in the observed data, that difference was 30%.

That's the 88% for the males, minus the 58% for the females.

And then we looked to see, does 30% appear to

be a usual outcome when we leave things up to chance?

Or does it not?

Each one of these dots here in the dot plot represents a

one simulated difference between the proportions

of males and females getting promoted.

30% does not seem like a usual outcome. In fact, it's quite unlikely to

obtain a result like the actual data,

or something even more extreme in these simulations.

More extreme meaning or something in the data meaning male

promotions being 30% more or even higher than female promotions.

Therefore we had decided to reject the

null hypothesis in favor of the alternative.

So to reminder ourselves of the framework.

We start with a null hypothesis that we usually

call it H naught and that represents our status quo.

And we also have an alternative hypothesis our HA that

represents our research question, in other word, what we're testing for.

We conduct a hypothesis test under the

assumption that the null hypothesis is true, either

via simulation, that's what we did at the

end of unit one, or using theoretical methods.

Methods that rely on the central limit theorem and

that's what we're going to do in this unit.