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 H0 : p = 0.8 versus the alternative, Ha : p < 0.8. Assume that the rejection region {y ≤ 12} is used. (a) In terms of this problem, what is a type I error?

Question

Timothy Kirk

Mathematics

4 July, 20:48

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 H0 : p = 0.8 versus the alternative, Ha : p < 0.8. Assume that the rejection region {y ≤ 12} is used. (a) In terms of this problem, what is a type I error?

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Christine Morrison · Answer 1

This type of error would lead to the conclusion that the dosage level is less effective than it really is.

Step-by-step explanation:

A Type I error happens when we reject the null hypothesis even when it is true.

In this case, this would happens when the sample taken gives results that end by pure chance in the rejection region, and nont because the null hypothesis is not true.

This type of error would lead to the conclusion that the dosage level is less effective than it really is.