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= $2,460. If required, round your answer to two decimal places.

(a)What are the sampling distributions ofxfor itemized deductions for this population of taxpayers for each of the following sample sizes: 30, 50, 100, and 400?

E(x)=$______ $

n (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 -

increases

does not change

reduces

Item 6

the standard error and results in a- Select your answer -

more

equally

less

Item 7

precise estimate of the population mean.