[All Steps] Let X_1,X_2,....,X_10 be ten observations of a certain normal random variable, with unknown mean and unknown variance. Suppose that the sample
Question: Let \({{X}_{1}},{{X}_{2}},....,{{X}_{10}}\) be ten observations of a certain normal random variable, with unknown mean and unknown variance. Suppose that the sample mean is 10.1 and the sample variance is \({{S}^{2}}\) is 0.0001
- Find the 95% confidence interval for the unknown mean
- Find the 95% prediction interval for the next observation (i.e. for \({{X}_{11}}\) )
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