1. Midterm Two (STAT 5432 - Spring 2010)
* * * Show your work to receive credit * * *
Due by 7:00pm on Tuesday April 13—
(Please Print Name) Last First
1. (30%) Let Xi, Xi, • • • , .Xie be iid random sample from a normal distribution JV(0, <r 2 ).
Find the UMP size a = 0.05 test for the following hypotheses and give explicit rejection
region for each test.
(a) HQ : a = 4 versus HI : a = 1.
(b) H0 : a < 1 versus #1 : a > 1.
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5. 2. (30%) Let Xi,X2, • • • ,XQ be iid random sample from a Bernoulli(p). Find the UMP
test for the following hypotheses and give explicit rejection region for each test.
(a) HQ : p = I versus H p = |, and the size a is close to 0.05.
(b) H0 : p < | versus HI : p > |, and the size a is close to 0.01.
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8. 3. (20%) Let Xi,X-2, • • • ,X-2§ be iid random sample from a normal distribution N(n, 1).
Find the UMP size a — 0.05 test of H0 : //, < 10 versus HI : // > 10 and give explicit
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4. (20%) Let Xi,X2,--• ,X-iQ be iid random sample from an exponential distribution
f ( x 0 ) = e--ex>x>Q. Find the UMP size a = 0.05 test of H0 : 0 > 100 versus
HI : 9 < 100 and give explicit rejection region for your test.
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