An experimenter has prepared a drug-dose level that he claims will induce sleep

Question

An experimenter has prepared a drug-dose level that he claims will induce sleep for at least 70% of people suffering from insomnia. After examining the dosage we feel that his claims regarding the effectiveness of his dosage are inflated. In an attempt to disprove his claim, we administer his prescribed dosage to 40 insomniacs and observe that 24 of them have had sleep induced by the drug dose. Is there enough evidence to refute his claim at the 5% level of significance? (Round your answers to two decimal places.)

3. Test statistic:  z =  

4. Rejection region:  If the test is one-tailed, enter NONE for the unused region.

Explanation / Answer

he sample proportion of people who have had sleep induced by the drug dose p^ = 24/40 = 0.6

here standard error of proportion se0= sqrt [ 0.70 * 0.30/ 40] = 0.0725

Teststatistic

Z = (p^ - 0.7)/ se0 = (0.6 - 0.7)/ 0.0725 = -1.38

Question 4

here rejection region for alpha = 0.05 significance level.

Zcritical = - 1.645

so Z < - 1.645

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