Question

Weight of totally pigs in a pig farm is 1357kg,5 of pigs are selected random. the amount of meat from each pigs:

Mass of pig                              Mass of meat

120kg                                        90kg

130kg                                        93kg

128kg                                        88kg

115kg                                        91kg

131kg                                        93kg

(a)Estimate bias ​ of the estimator of the mass of meat per unit mass of pigs.

(b) 95%CI for mass of meat per unit of pigs.

Answer 1

Total weight of all pigs = 1357 kg Sample size = 5 pigs (a) Bias of estimator of mass of meat per unit mass of pigs Bias = Expected value of mass of meat per unit mass of pigs - Mass of meat per unit mass of pigs Expected value = (90/120 + 93/130 + 88/128 + 91/155 + 93/131)/5 = 0.75 + 0.71 + 0.68 + 0.79 + 0.71/5 = 0.728 kg mass of meat per unit mass of pigs Mean Bias = .015/5 = 0.003 (b) 95% C.I. for mass of meat per unit pig Total mass of meat of 5 pigs = 455 Mass of meat per unit pig = 91 kg z value for 95% C.I = 1.96 n = 5 sigma = sample standard Deviation sigma = squareroot sigma(x - x^bar)^2/n sigma = squareroot (90 - 91)^2 + (93 - 91)^2 + (88 - 91)^2 + (91 - 91)^2