3a) An engineering consulting firm wanted to evaluate the diameter of rivet heads. The following data represent the diameters (in hundredths of an inch) for a random sample of 10 rivets. 6.81, 6.69, 6.69, 6.59, 6.65, 6.60, 6.74, 6.76, 6.84, 6.81 The above data numerical summary is as follows: IM * =67.18 and > x? = 451.3858 (i) Calculate a point estimate of the mean diameter of rivet heads for all rivets in the population. (ii) Calculate point estimate of the proportion of rivets in the population that have diameter greater than 6.69. (iii) Calculate an estimate of the standard error of the point estimate from part (i). Points (10) 3b) Suppose O, and O, are estimators of the parameter 0. We know that E(0,) = 0,E(02) = 20, Var(0, ) = 10 and Var(02) = 6. Are O, and O, unbiased estimators of the parameter 0? Why? (i) Is Theta 1 hat unbiased estimator of parameter theta. Choose one (Yes or No) (ii) Is Theta hat 2 unbiased estimator of parameter theta. Choose one (Yes or No) iii) Which of the two estimators of the parameter theta you prefer if theta = 1.5? Why