Question

Pennies minted after 1982 are made from 97.5% zinc and 2.5% copper. The following data represent the weights (in grams) of 17 randomly selected pennies minted after 1982. 2.46 2.47 2.49 2.48 2.50 2.44 2.46 2.45 2.49 2.47 2.45 2.46 2.45 2.46 2.47 2.44 2.45

a) Use an unbiased estimator to compute the point estimate of the population mean weight of pennies minted after 1982.

b) Use an unbiased estimator to compute the point estimator of the population proportion of all pennies minted after 1982 over 2.45 grams.

Answer 1

a. Sample mean is unbiased estimator of population mean and its value is

b. Let us first arrange daa in ascending order

2.44   2.44   2.45   2.45   2.45   2.45   2.46   2.46   2.46   2.46   2.47   2.47   2.47   2.48   2.49   2.49   2.50   

Here we find 11 values above 2.45

So unbiased estimator of population proportion is