Statistics, need help ASAP? 1. Let X1.x2 be a random sample (iid) of sze n = 2,

Question

Statistics, need help ASAP? 1. Let X1.x2 be a random sample (iid) of sze n = 2, where the common pdf is a (1,0) pdf with unknown. we are interested in testing Ho : = 1 versus H1 : = 2. Let T = X1 + X2. Our test is given by Reject H0 : = 1 and accept Hi :-2,ifT>3. For the following questions, use Theorem 3.3.2 on page 161. (a) Using Theorem 3.3.2, what is the distribution of the test statistic T if Ho is true? (b) Using R determine the level of the test; i.e., determine a where (c) Using Theorem 3.3.2, what is the distribution of the test statistic T if H, is truef? (d) Using R determine the power of the test, i.e., determine where (e) Here are 5 such samples. Determine the decision using the test (l). Sample Decision 1 0.943 0.282 2 1.788 0.454 3 3.357 2.203 4 1.551 2,822 0.735 2.233 (f) Suppose Ho is true for these 5 samples what is the estimate of based on the results?

Explanation / Answer

1.a) T = X1 + X2, where X1,X2 ~iid (1,).
Thus, T ~ (2,) due to the reproductive property of gamma distribution.
Thus, under H0, T ~ (2,1).

b) > alpha=pgamma(3,2,1,lower.tail=F)

> alpha

[1] 0.1991483

c) Under H1, due to the reproductive property of gamma distribution, T ~ (2,2).

d) > gama=pgamma(3,2,2,lower.tail=F)

> gama

[1] 0.01735127

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