Problem 5: 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. Consider the test Ho: Item is of type A versus Ha: Item is of type B. a) Calculate the likelihood ratio statistic of this test. 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 of this test? d) What is the power of this test? (Hint: Compute the power using its definition.) e) What is the p-value when X = 120? (Hint: Values as extreme or more extreme than the observed value are X ≥ 120.)