The life in hours of a bettery is known to be approximately normally distributed

Question

The life in hours of a bettery is known to be approximately normally distributed, with a standard deviation 1.25 hours. A random sample of 10 batteries has a mean life of 40.5 hours. Is there evidence to support the claim that battery life exceeds 40 hours?

A) test the appropriate hypothesis at level of significance 0.05

B)what is the power of the test when m=42

C)what is that smallest level of significance at which the null hypothesis can be rejected for this sample?

D)Suppose sigma is unkown. The standard deviation of the sample of 10 batteries was 1.1 hours. Test the hypotheses of (A)

Explanation / Answer

sample mean life =40.5
population stdev=1.25
n=10

a)

Ho: life=40
H1: battery life>40

z0= (40-40.5)/1.25/?10

= -1.26

z(at .05) = 1.64

z0<z(at .05)

Ho true at .05 significance level . Battery life is <=40 hrs

b) p value =.1038

c)z=(40-41)/1.25/?10

=-2.53

p value = .0057

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