An experimenter has prepared a drag dosage level that she claims will induce sle

Question

An experimenter has prepared a drag dosage level that she claims will induce sleep for at least 75% of people suffering from insomnia. After examining the dosage, you feel that her claims regarding effectiveness of the dosage are inflated. In an attempt to disprove her claim you administer her prescribed drug dosage to 35 insomniacs, and observe Y. the number for which the drug dose induced sleep. You wish to test the hypothesis H_0 : p = 0.75 vs. H_a : p lessthan.75. Assume that the rejection region RR :{Y lessthanequal 20} is used. In terms of this problem, what is a type I error? Find alpha. In terms of this problem, what is a type II error? Find beta when p =.52. Find beta when p =.38. Suppose now that the rejection region is of the form RR : {Y lessthanequal k}. Find the value of k so that a is no greater than 0.10. For the rejection region found in (f), find beta when p = 0.52. For the rejection region found in (f), find beta when p = 0.38.

Explanation / Answer

(a)
If the experimenter concludes that less than 75% of insomniacs respond to the drug when actually
the drug induces sleep in 75% of insomniacs, a type I error has occurred.

(b)
= P(reject H0 | H0 is true) = P(Y 20 | p = .75) = ___(Look for the probability when n =35 and a = 20.(use binomial distribution formula))

(c)
If the experimenter does not reject the hypothesis that 75% of insomniac respond to the drug when
actually the drug induces sleep in fewer than 75% of insomniacs, a type II error has occurred.

(d)
(.52) = P(fail to reject H0 | Ha is true) = P(Y 20 | p = .52) = 1 - P(Y 20 | p = .52)=___

(d)
(.38) = P(fail to reject H0 | Ha is true) = P(Y 20 | p = .38) = 1 - P(Y 20 | p = .38)=____

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