e wish to test an effect of a drug that claimed to improves the patients with 80% of chance. The drug is given to 20 patients and we observed the number Y of people who improved. The hypothesis is: H0 : p = 0.8 vs H1 : p < 0.8. Use the rejection region RR = {y ≤ 12} and answer question a-e. a) State type I error in terms of Y and p. b) Find α. c) State type II error in terms of Y and p.
We wish to test an effect of a drug that claimed to improves the patients with 80% of chance. The drug is
given to 20 patients and we observed the number Y of people who improved.
The hypothesis is:
H0 : p = 0.8 vs H1 : p < 0.8.
Use the rejection region RR = {y ≤ 12} and answer question a-e.
a) State type I error in terms of Y and p.
b) Find α.
c) State type II error in terms of Y and p.
d) Find β when p = 0.
e) Find β when p = 0.
f) Find the rejection region {y ≤ c} with α ≈ 0.
g) For the rejection region in f), find β when p = 0.
h) For the rejection region in f), find β when p = 0.
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We wish to test an effect of a drug that claimed to improves the patients with 80% of chance. The drug is
given to 20 patients and we observed the number Y of people who improved.
The hypothesis is:
H0 : p = 0.8 vs H1 : p < 0.8.
Use the rejection region RR = {y ≤ 12} and answer question a-e.
d) Find β when p = 0.
e) Find β when p = 0.
f) Find the rejection region {y ≤ c} with α ≈ 0.
g) For the rejection region in f), find β when p = 0.
h) For the rejection region in f), find β when p = 0.
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