Question

For the year 2010, 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,642. Assume that the standard deviation is σ = $2,500. If required, round your answer to two decimal places.

(a)	What are the sampling distributions of x for itemized deductions for this population of taxpayers for each of the following sample sizes: 30, 50, 100, and 400?
	E(x) = $
	n σ(x) 30 $ 50 $ 100 $ 400 $
(b)	What is the advantage of a larger sample size when attempting to estimate the population mean?
	A larger sample - Select your answer -increasesdoes not changereducesItem 6 the standard error and results in a - Select your answer -moreequallylessItem 7 precise estimate of the population mean.

Answer 1

a) σ = $2500

σ(x) = σ/√n

n	σ(x)
30	2500/√30 = 456.44
50	2500/√50 = 353.55
100	2500/√100 = 250
400	2500/√400 = 125

b) A larger sample reduces the standard error and results in a more precise estimate of the population mean.