The intensity of light reflected by an object is measured. Suppose there are two types of possible objects, A and B. If the object is of type A, the measurement is normally distributed with mean 100 and standard deviation 25; if it is of type B, the measurement is normally distributed with mean 125 and standard deviation 25. A single measurement is taken with the value X = 120.
a. What is the likelihood ratio?
b. If the prior probabilities of A and B are equal ( 1/ 2 each), what is the posterior probability that the item is of type B?
c. Suppose that a decision rule has been formulated that declares the object to be of type B if X > 125. What is the significance level associated with this rule?
d. What is the power of this test?
e. What is the p-value when X = 120?
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