Problem 6: Suppose we observe a random variable X~ Binomial(n, p). (a) What is the generalized likelihood ratio for testing Ho: p = 0.5 against H₁ : p‡ 0.5? (b) If we will reject Ho when |X - n/2 ≥ d (that is, we reject Ho when X is either to small or too large), what is the significance level of the test when n = 3 12 and d = 5? Hin use binomial distribution to compute the probability.

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Problem 6: Suppose we observe a random variable X~ Binomial(n, p).
(a) What is the generalized likelihood ratio for testing Ho : p = 0.5 against H₁ : p0.5?
(b) If we will reject Ho when |X - n/2 ≥ d' (that is, we reject Ho when X is either too
small or too large), what is the significance level of the test when n = 12 and d' = 5? Hint:
use binomial distribution to compute the probability.
Transcribed Image Text:Problem 6: Suppose we observe a random variable X~ Binomial(n, p). (a) What is the generalized likelihood ratio for testing Ho : p = 0.5 against H₁ : p0.5? (b) If we will reject Ho when |X - n/2 ≥ d' (that is, we reject Ho when X is either too small or too large), what is the significance level of the test when n = 12 and d' = 5? Hint: use binomial distribution to compute the probability.
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