The expected mean of a normal population is μ0

, and its standard deviation is 10. a sample of 25 measurements gives a sample mean of 96. using the α = .01

level of significance a test is to be made to decide between "population mean is 100"

or "population mean is different than 100."

a)state null and alternative hypotheses 1p

b)what conclusion can be drawn at the at the given level of significance α = .01? 3p

c)what conclusion can be drawn if α = .05? 1p

d)what is the p-value of the test? give the definition of p-value. 3p

e)what is probability of type ii error when μ really is 97 and α = .05 ? 2p

f)give the definition of type i and ii errors. how can we control them? 2p

g)how many measurements need be made so that on the 5% level of

significance hypotheses h0

if real value of μ is 97, μ = 97.? 2p

h. does the population need to be normally distributed in order to test

the claim using the methods of our course?

when normality of distribution is not necessary? 2p

, μ0 = 100 , has a 80% probability of rejection