Rejecting the Null Hypothesis

Hi,

This has been bothering me for a while, so I thought I'd get some help from the TSR community, as my teacher can't seem to answer it.

Could somebody please try answering this as thoroughly as possible?

Why do we reject the null hypothesis when the p value is less than the significance level?

For example, in the question above, why is the null hypothesis rejected when P (x<= 0.08)<0.05 ?

I thought that we'd reject the null hypothesis when P (x<= 0.08)>0.05 ?

Thank you in advance for all the help!

In every hypothesis test you have your null hypothesis $H_0$ which is the boring statement about what you have observed over long periods of time. It becomes your go-to statement.

You also have the more exciting alternate hypothesis $H_1$ which aims to challenge $H_0$, but before we sway to reject $H_0$ in favour of $H_1$, we need to mathematically establish when it is acceptable to do so.

If you observe an event taking place in a particular sample, then you need to see what the likelihood of this event occuring is if you assume $H_0$ to be true.

Now the kicker is that if the probability of this event happening is VERY small, i.e. below a certain treshold which we denote as the level of significance, then it should make you think that it is extremely unlikely that this event has occured purely due to luck, and thus it is a statistically significant result because it suggests a shift away from the null hypothesis.

If this turns out to be true, i.e. p value is less than sig level, then you reject the null hypothesis as it is not longer a suitable statement. You do not accept the alternate hypothesis however either as you need to be careful.

P.S. This might help you understand a bit more: https://opentextbc.ca/researchmethods/chapter/understanding-null-hypothesis-testing/