How to Determine Whether to Accept or Reject a Hypothesis?

[physicslady123]

Summary:: Confused on correction for contunuity

I'm confused about one step for questions like this where you have to determine to accept or reject the null hypothesis.
Sample size: 50
Number of successes: 23
Significance level: 10%
Null hypothesis: p = 0.4
Accepted hypothesis: p > 0.4

Solution:
μ = np
= (50)(0.4)
= 20

σ = √npq
= √(20)(0.6)
= 3.46

This is the part I'm confused on: To determine if I should accept/reject the hypothesis, would I do 1) or 2) or 3)

1) P ( x̅ >23)
= P ( x̅ > 23.5)
= 1-P(x̅<23.5)
and then solve

2) P ( x̅ >23)
= 1 - ( x̅ < 22.5)
and then solve

3) P ( x̅ < 23)
=P ( x̅ < 22.5)
and then solve

 

[Office_Shredder]

Why do you have to introduce 22.5 and 23.5 at all? Can't you just look at $P(\bar{x} \geq 23)$?

What is your plan with the $\sigma$ you computed? Typically that means you are going to pretend that the values you are drawing are from some t distribution or something, and the fact that it's integer valued no longer is as much of an issue, since in the approximation the integers are not special values.

 

[pbuk]

Why do you have to introduce 22.5 and 23.5 at all? Can't you just look at $P(\bar{x} \geq 23)$?

What is your plan with the $\sigma$ you computed? Typically that means you are going to pretend that the values you are drawing are from some t distribution or something, and the fact that it's integer valued no longer is as much of an issue, since in the approximation the integers are not special values.

I would guess that in the question the samples are drawn from a binomial distribution and so the fact that it is integer valued is important. This question belongs in the homework section, I'll get it moved.