Question

Basic Inferential Statistics Question (Screenshot will be commented). Really, I can solve the problem myself, I just need clarification on one part of it.

Answer 1

My main question is what 'x' stands for in the question. Is there some sort of statistical convention for what 'x' would mean in this question?

Answer 2

x looks like it is a random value from that distribution

Answer 3

in this case, alpha is ridiculously high (when it's normally a lot smaller)

Answer 4

If x is the random variable of the distribution, then I'd assume that it'd be for the normal distribution since we're testing hypotheses, right?

Answer 5

yes correct

Answer 6

So, that'd mean that we'd reject the null if p > 50%?

Answer 7

you reject the null if x > 0

x = 0 is the center so 50% of the values fall on one side of the mean, while 50% lie on the other side

which is why alpha =0.5

if you reject the null, and if the null is true, then you have a 50% chance of doing this

Answer 8

Ok, that makes sense. And since alpha is the probability of type I error, (a) is 0.5.
Then (b) would be when the null hypothesis isn't rejected when it is actually false, right?

Answer 9

yeah a type 2 error is where you fail to pick Ha as the correct hypothesis when it is true

Answer 10

Ok, thanks for the clarification!

Answer 11

np