Question

Each of 161 newly manufactured items is examined and the number of scratches per item is recorded (the items are supposed to be free of scratches), yielding the following data: Number of scratches per item Observed frequency 12 44 35 33 12 12 8 5 0 123 4 5 6 7 Let X the number of scratches on a randomly chosen item, and assume that X has a Poisson distribution with parameter μ (a) Find an unbiased estimator of μ and compute the estimate for the data. [Hint: E(X) = μ for X Poisson, so E(X) = ?] (Round your answer to two decimal places.) (b) What is the standard deviation (standard error) of your estimator? Compute the estimated standard error. [Hint: σ/ = μ for X Poisson.] (Round your answer to three decimal places.)

Answer 1

Solution-

(a) Unbiased estimator of population mean = sample mean =

= $\frac{\sum f* X_{i}}{\sum f}$

= 404/161

= 2.5093

(b) Standard deviation of X = 2.5093^0.5 [ variance = mean = 2.5093 ]

= 1.5841

Standard error of sample mean =

standard deviation / n^0.5

= 1.5841/161^0.5

= 0.1248

Answers

TY!