To test a new drug, a group of 10 matched pairs of volunteers is used. In each p

Question

To test a new drug, a group of 10 matched pairs of volunteers is used. In each pair, one volunteer is treated with the drug while the other is treated with a placebo as control. At the end of the double-blind experiment, a physician examines each pair and declares which of the two is healthier. Let K be the number of pairs in which the treated patient was declared healthier than the control. The null hypothesis is that the drug is absolutely ineffective (neither good or bad). It has been decided to reject H0 whenever K > 8.


(a) Find , the probability of a type I error.
(b) Suppose that the drug is so effective that for each matched pair, the probability is 90% that the treated patient will be declared healthier. Find , the probability of a type II error.

Explanation / Answer

a) rejecting the null when it is true. So if it were true, we would be equally likely to choose either, or .5 for each. We assume they have to pick one. 10 Choose 8 * .5^8*.5^2+10 Choose 9 * .5^9*.5^1+10 Choose 10 * .5^10=7/128=.055 b) so we assume .9 is the one probability. we now want K

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