# Selection of n in a binomial distribution hypothesis testing problem

Was trying to solve this problem but have hit a wall.

A psychiatrist believes that more than 50% of the users of sleeping pills sleep better simply because of the psychological effect of taking the pills. To substantiate this hypothesis with data, he selects a random sample of 20 insomniacs and gives each of them a box of pills to use. They are actually sugar pills but are otherwise identical to a popular brand of sleeping pills currently on the market. Subsequently, 15 of these patients report that the pills have been effective in inducing sleep. Assuming a level of significance close to 0.05, does this observation support the psychiatrist's conjecture.

Ok, so here is my interpretation of the problem:

1. H0: The number of patients who sleep better with the help of sleeping pills is > 50%
2. H1: The number of patients who sleep better with the help of sleeping pill is <= 50%
3. Rejection region is X >= 15
4. alpha <= 0.05
5. Distribution is binomial b(20,0.5)

Now to solve this I look up the CPD tables for binomial distribution where:

The tables are P[X <= c] so P[X>=15]=1-[X<=14]=1-0.979=0.021 since 0.001 << 0.05 H0 is false and hence the conjecture of the psychiatrist true

However when I look up the answer key at the back of the book is says:

Rejection region X >=14 has an alpha of 0.058, claim is supported

Now I can't understand how he arrived at the rejection region being X >= 14

-
I think you have null and alternative backwards. (At the very least, equality should be in the null.); Also I believe you should add the homework tag. I'd do it myself but you should have the chance to explain how it shouldn't count as homework. – Glen_b Oct 21 '12 at 23:52