When a person is well, the test result for a certain disease is normally distrib

Question

When a person is well, the test result for a certain disease is normally distributed with mu = 10 (null hypothesis) and sigma = 2. For individuals with the disease, the mean test result is also normally distributed with mu = 15 (alternative hypothesis) and mu = 2.
We classify a person as not having the disease if the test result does not exceed c and having the disease if the test result exceeds c. Of course, this classification produces errors: classifying a non-diseased person as having the disease and a person that has the disease as not having the disease.

a) What must c have to be if alpha = .05?

b. Based on the value of c in part a) what is the probability of a Type II error?

c. What would be the P-value for a test result of 14?

Explanation / Answer

a) value for c for alpha =.05

c=Mu+z(.95)*Sigma = 10+1.65*2 = 13.3

b) beta is prob of type II error:

=NORMDIST(13.3,15,2,true) = 0.198

c) P-value for a test result of 14:

=1-NORMDIST(14,10,2,TRUE) = 0.023

(we used excel)

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