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LetXibe the i th observation of variable X in a random sample of size n. Suppose E(X)= and V(X)=>0. LetX=1/n n i=1 Xi 1) Find

LetXibe the i th observation of variable X in a random sample of size n. Suppose E(X)= and V(X)=>0. LetX=1/n n i=1 Xi

1) Find the approximate distribution ofX-

2)Based on the result above, find a statistic to test the hypothesis that=

o.Choose a statistic that follows standard normal distribution under the hypothesis.

3)Suppose n=100,x=1200, and =2000.Test the hypothesis that =1000 at 5% significance level. Choose the one that best describes your result.

4)Find the 95% confidence interval for .

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