Hypothesis testing query

[apple2357]

Consider the following question:


This is Binomial model with n=10, p=1/4
The Null Hypothesis would p=1/4 and the alternate one would be p>1/4
I get all that.

And when we are performing the test we look at P(X>=5) and compare this probability to the significance level and use this to determine whether to reject or accept the null hypothesis. This appears the standard way. The question I have is why do we not look at P(X=5) which is what the question refers to, to determine whether to reject/accept?

 

[Dr.Peterson]

This is Binomial model with n=10, p=1/4
The Null Hypothesis would p=1/4 and the alternate one would be p>1/4
I get all that.

And when we are performing the test we look at P(X>=5) and compare this probability to the significance level and use this to determine whether to reject or accept the null hypothesis. This appears the standard way. The question I have is why do we not look at P(X=5) which is what the question refers to, to determine whether to reject/accept?

First, I'm curious how you know to use P(X>=5) rather than P(X=5). Does your textbook give an explanation? I'd look for that first. I hope they don't just decree it!

But in general, the probability you are looking for is "the probability that something at least this unusual would happen under the null hypothesis". This is more obvious when you are working with a normal distribution, where the probability that exactly what occurred will happen is zero, so you have to go with the inequality. But the same thinking applies here.

 

[apple2357]

Thanks. It did offer something along the lines that we look for the prob of at least X=5 because X=6,7,8,9,10 is even less likely but it didn't make complete sense to me because it's possible to work out P(X=5). However, when working with normal distribution it makes more sense.