Problem 2. Suppose each X; for i = 1,2,... is independently drawn from the same normal distribution with unknown mean and unknown variance. We wish to find a confidence interval for the mean. Suppose we have n = 6 data points, with values: X₁ = 1 X2=2 X3 = 4 X4=0 X5 = 2.5 X6 = 10 (a) Calculate the sample mean: X = 牌 Xi (b) Calculate the sample variance: 1 n-1 n Σ(X-X)² i=1 (c) Find a 95% confidence interval for the population mean μ.

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