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Suppose that X . . . . . Xn is a random sample from a normal population with unknown mean μ x and unknown variance σ I. What is the form of a 95% confidence interval for μχ . Îs your interval the shortest 95% confidence interval for μχ that is avail- able? 2. What is the form of a 95% confidence interval for . Is your interval the shortest 95% confidence interval for σ, that is avail- able? 3. Use the previous result to find a suitable 95% confidence interval for the population standard deviation f you now obtain a sample of n sample mean of 12.28 and a sample standard deviation of 3.3585, provide the corresponding confidence intervals for each ofAx, ơ and σχ 4. I -32 observations, resulting in a 5. Discuss why the intervals described above are considered as ran- dom intervals with associated probability of containing the true parameter of 0.95, whereas the corresponding confidence interval calculated from the 32 observations either does or does not contain the true parameter value with probability I

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