High cholesterol is diagnosed if the mean level in blood is over 240. The amount

Question

High cholesterol is diagnosed if the mean level in blood is over 240. The amount of cholesterol in a blood sample varies from sample to sample but is normally distributed with mean which is unknown and standard deviation 10 we test the hypothesis s 24 against 240 Suppose 2 100a samples are taken and the sample mean evaluated. The hypothesis test is done at the 5% level. A person is said to have very high cholesterol if their mean level is over 260. What is the chance (power) of detecting a person with very high cholesterol when using this hypothesis test? 100% 88% 50% 5% 6096

Explanation / Answer

1)at 5% level ; critical value of z =1.6449

std error of mean =std deviation/(n)1/2 =10/(2)1/2 =7.07

for rejection region =240+1.6449*7.07 =251.63

therefore power =P(X>251.63)=1-P(X<251.63)=1-P(Z<(251.63-260)/7.07)=1-P(Z<-1.1836)=1-0.1183 =0.8817

~ 88%

2)

from above probability that a person is not detected =typr II error =1-Power of the test =1-0.88 =0.12 ~ 12%

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