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 = $2,220. 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?

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

Given that ,

Mean ammount of deduction of taxpayers was with a deviation of

(a)

Let

Now , for

Now, for

Now , for

Now, for

Hence we get

(b)

The larger sample size gives smaller standard error, value of has less variation and tend to be closer to population mean compared to it.