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 $$16,642.$ Assume that the standard deviation is $\backslash$sigma $=$ $$2,400.$ If required, round your answer to two decimal places.

$($a$)$ What are the sampling errors 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 $\backslash$sigma 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 $-$

the standard error and results in a$($n$)$

$-$ Select your answer $-$

precise estimate of the population mean.