Question

An experimenter has prepared a drug dosage level that she claims will induce sleep for 80% of people suffering from insomnia. After examining the dosage, we feel that her claims regarding the effectiveness of the dosage are inflated. In an attempt to disprove her claim, we administer her prescribed dosage to 20 insomniacs and we observe Y, the number for whom the drug dose induces sleep. We wish to test the hypothesis Ho: p = .8 versus the alternative, H:p <.8. Assume that the rejection region {y < 12} is used. a In terms of this problem, what is a type I error? b Find a. c In terms of this problem, what is a type II error? d Find ß when p = .6. Find B when p = .4. e

Answer 1

cal An The hull and alternative hypotheses are Ho: p=0.8 vs Hap<0.0 The rejection eregion in (4212², where y be the no. of people for whom drug close induces sleep Then for 20 insomanics, y - Binomial (n=20, P). with mean E(V)= np s vanix) = 0 = Inpu-p) The type I error would occure if one rejects & the claim of the experimenter that drug dosage level will induce sleep for 80 l. of people suffering from insomnia despite it is being true. () The level of significance a in given by da prltype I emor] - Prireject Ho while it is true] - Pr [ Y 312 1 P=0.8] when Yu Binomial (20,0-8) u 0,03 I 0.0.8,12 (0.220-12 J2 x=0

The B can (CI The type II error would be occur if one do not reject the claim of the experimenten that the drug dosage level will induce sleep for 80% of people suffering from insomnia despite the claim is not true and inflated. (d, be defined as B = Dr I dype II error] = Polaccept Ho 'while it in false] = Pr ( 7 > 121 P=0.6 ] yu Binomial (n=20, P=0,6) - Ž (0,6)'2 (0.430-12 (7 ♡ 0,4159 X.73 (e) ß when p=0.4 B = Pr [accept Ho while Ho is false] where Yu Binomial (n=20, P=0.4) Epr ( Y>12 | P=0.4 ] u 0.0210 I (230) (0.4/12 (0.6) 20 20-12 20 20:13