Problem 1. Assume, the observations X1, X2, . . . , Xn are iid. normal distributed...

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Problem 1. Assume, the observations X1, X2, . . . , Xn are iid. normal distributed...

Problem 1.

Assume, the observations X1, X2, . . . , Xn are iid. normal distributed random variables with unknown mean θ. You observe n = 16 many variables with the empirical mean 1.45 and a sample variance of 0.512.

a) Determine a 90% two-sided confidence interval for the mean.

b)HowcanwedecideonthehypothesisH0 :μ=2vsH1 :μ̸=2onthe significance level 10%, using just the answer for part a) and no additional computations?

c) Now assume that, instead of using the sample variance, you know that the variance of the observed random variables X1, . . . , Xn is 0.52? What is the confidence of the confidence interval [5/4, 13/8]?

math Statistics-And-Probability

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