Question 1 (15 marks) Given the following dataset: 12.62 14.31 10.71 12.49 7.26 11.65 12.43 12.03 14.00 13.82 (a) If the population distribution is normal, state the minimum variance unbiased estimator of the mean. Then, compute the corresponding point estimate. Round your answer to 3 decimal places. (b) Write down the formula for the standard error of X. Is it possible to obtain the standard error of X? If yes, perform the computations and round your answer to 3 decimal places. Otherwise, explain why it is not possible to do so. (3] (c) Write down the formula for the estimated standard error of X. Is it possible to obtain the estimated standard error of X? If yes, perform the computations and round your answer to 3 decimal places. Otherwise, explain why it is not possible to do so. (3] (d) Compute and interpret an appropriate 90% confidence interval for the true average. Ensure that the number of decimal places in your final answer follows the number of decimal places of your point estimate. (e) Would you expect a wider or narrower interval if you were to compute a 95% confidence interval? Explain your answer without constructing another confidence interval. (3)