For the following problem, I have solved a through c, and used a summation of combinations to solve for alpha (0.009982); I received an answer that solved for beta values using a z score table, but I don't think that's right - wouldn't I use combinations to solve for the beta values, as well? Can someone answer d through f using this method?
An experimenter has prepared a drug dosage level that she claims will induce sleep for 80% of the people suffering from insomnia. After examining the dosage, we feel that her claim regarding the effectiveness of the dosage is inflated. In an attempt to disprove her claim, we administer her prescribed dosage to 20 insomniacs, and we observe Y, the number for which the drug dose induces sleep.We wish to test the hypothesis H0: p = 0.8 versus the alternative Ha: p < 0.8 with rejection region Y< 12.
a) In terms of this problem, what is a type I error?
b) Find the level, alpha.
c) In terms of this problem, what is a type II error?
d) Find beta when p = 0.6
e) Find beta when p = 0.4
f) Find alpha and beta (p=0.6) when we use rejection region y<15