1. Briefly answer the following questions. (a) Suppose that a commonly-used slee

Question

1. Briefly answer the following questions. (a) Suppose that a commonly-used sleeping pill makes 70% people sleep 7 hours or more. A new drug is introduced and claims to be more effective than the popularly used one. Formulate the null hypothesis and alternative hypothesis. What are the type I and type II errors in this context? (b) A manufacturer of 40-amp fuses wants to make sure the mean amperage at which its fuses burn out is in fact 40. What null and alternative hypotheses would be of interest to the manufacturer? Describe type I and type II errors in the context of this problem? (c) True of False (i) P-values are the chance that null hypothesis is true (ii) When P-value is 0.005, the null hypothesis looks plausible. (iii) When P-value is 10%, the null hypothesis cannot be rejected.

Explanation / Answer

a)
The hypothesis is

H0 : The new drug makes 70% people sleep 7 hours
H1 : The new drug makes 70% people sleep more than 7 hours

Type 1 error is
Reject null hypothesis , when we should not

So error would be if we conclude The new drug makes 70% people sleep more than 7 hours when in fact The new drug makes 70% people sleep 7 hours is true

Type 2 error is
Accept null hypothesis , when we should not

So error would be if we conclude The new drug makes 70% people sleep 7 hours when in fact The new drug makes 70% people sleep more than 7 hours is true

b)

H0 : The mean ameperage of fuses burn out is not 40
H1 : The mean ameperage of fuses burn out is 40

Type 1 error is
Reject null hypothesis , when we should not

So error would be if we conclude The mean ameperage of fuses burn out is 40 when in fact The mean ameperage of fuses burn out is not 40 is true

Type 2 error is
Accept null hypothesis , when we should not

So error would be if we conclude The mean ameperage of fuses burn out is not 40 when in fact The mean ameperage of fuses burn out is 40 is true

c)
i) true , as from the defintion of type 1 error
ii) no , there is only 0.5% chance that the null hypothesis is true
iii) true , assuming alpha of 0.05 , if p value is 0.1 then we cant reject the null hypothesis

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