Question

A “treat” delivery system was being developed to study determination among monkeys as well as decision making. The monkey could either turn a knob or lift a lever to engage the delivery system, which often would deliver a small rock and only sometimes a treat. The monkeys were trained to know both the knob and lever would deliver something. Whether the monkey turned the knob or lifted the lever engaged the delivery system in an identical way. Each attempt was independent of previous attempts. To tune the mechanical system, a researcher wanted to first know that the delivery probability was at least 0.20. She decided that a quick test would be if one monkey engaged the delivery system 10 times in succession without a treat, and she would then declare that the treat delivery probability is less than 0.20; otherwise, it would be accepted as at least 0.20. (a) What was the Type I error that the researcher was accepting? (b) Plot the power curve for this test over the alternative hypothesis range, with p>0.

Answer 1

Solution : Nell hypothesis Ho: P20.20 Alternative hypothesis Ho: P20.20 When Ho is Towe, assuming probability of delivery treat = 0.20 Type I error = P(Reject Holto is free) = (1-0.2010 (No treat delivery in to trials) 20.10th when Ho is false, assuming probability of delivery treat =P where P20.20 Power = P(Reject Holho is false) = (1-pjo The plot curre for alternative hypothesis ranges is, Power curve 0 80 90 10 20 0.05 Oilo 0.15 0.20 0.00 Scanned with CamScanner Р