Question

Suppose that we want to know the mean income of residents in Brazos County. Call this mean income μY. We cannot afford to survey every person in Brazos County, so we decide to randomly select 100 people and ask their income. This yields a sample of 100 random variables {Y1, Y2, ..., Y100}. You suggest taking the sample average of all 100 observations as your estimate of ^μY . Your statistics friend suggests taking the 37th observation (Y37) as his estimate of ^μY .

(a) Show explicitly whether or not your estimate outperforms his estimate in terms of unbiasedness.

(b) Show explicitly whether or not your estimate outperforms his estimate in terms of efficiency.

Answer 1