Find the maximum livelihood in the following values

The breaking shengthe of cables produced by a certain manufacture have a mean, ju. of 1875 pounds, and a standard deviation of 95 points. it to chamand that an improvement in the manufacturing process has increased the mean breaking strength, To evaluate this chain, 20 newly manufactured cables me randomly chingen and tested, and then mean breaking strength is found to be 1830 pounds. Assume that the population is formally distributed, Can me support, at thre DI barlet imunificance. the claim that the mean treating Strength Has moreused? (Assume that the standard deviation has not changed. ) Perform as possdated tell Then complete the parts below. Carry your intermedute computations to these or more decimal places, and round your responses ar specified below. (If necessary, consult a fat of formulas. ) (2) State the pull Ivbothears Ho and the alternative barpothesis Is O HOW (0) Determine the type of test striving to use (Choose one] T (c) Find the value of the test stansbe. (Round to thice or more decimal places.) (di Find the pmake! (Round to three or more deamal places. ).Question 1 (1 point) + x)""-', for r > 0, a > 1 and > > 0. Suppose that that A is known to be equal to 50. (a) Find the maximum likelihood estimate for a. [4] (b) Find a method of moments estimator of a. [4] (c) A firm collected data on the size of claims and the following data were collected: 24, 40, 60, 72, 100 It is assumed that A = 50. Compare the values of both estimators of a. [3] (d) Provide an approximate 95% confidence interval for a. [4] [Total = 15] @UCD 2015/16/Modular 2 of 6 4. The time between trades of a company's shares are well modeled as indepen dent observations from an exponential distribution with mean 0. fx(x) = - exp (-7) , for a > 0. (a) Find the maximum likelihood estimator for the mean, 0. [3] (b) Compute the bias, variance and mean squared error of the estimator. [4] (c) Derive the Cramer-Rao lower bound and comment on the performance of the estimator proposed in (a). [5] (d) A trader recorded the time (in minutes) between trades in a company's shares. The data she recorded is as follows: 0.3 28.9 1.6 25.9 5.4 6.9 Estimate o and report a standard error for the estimate. [3]