The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. Themean amount of deductions for this population of taxpayers was $16,642. Assume the standard deviation is o =$2,400.(a) What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean foreach of the following sample sizes: 20, 60, 100, and 300? (Round your answers to four decimal places.)sample size n = 20sample sizen =60sample sizen = 100sample size n = 300(b) What is the advantage of a larger sample size when attempting to estimate the population mean?A larger sample has a standard error that is closer to the population standard deviation.A larger sample increases the probability that the sample mean will be within a specified distance of the population mean.A larger sample increases the probability that the sample mean will be a specified distance away from the population mean.A larger sample lowers the population standard deviation.

Answered: The Wall Street Journal reports that…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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The Wall Street Journal reports that 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 the standard deviation is o =
$2,400.
(a) What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean for
each of the following sample sizes: 20, 60, 100, and 300? (Round your answers to four decimal places.)
sample size n = 20
sample sizen =
60
sample sizen = 100
sample size n = 300
(b) What is the advantage of a larger sample size when attempting to estimate the population mean?
A larger sample has a standard error that is closer to the population standard deviation.
A larger sample increases the probability that the sample mean will be within a specified distance of the population mean.
A larger sample increases the probability that the sample mean will be a specified distance away from the population mean.
A larger sample lowers the population standard deviation.

Expert Solution

Step 1

In this question, we need to calculate the probability of a sample of taxpayers from the income group. Here we can use the formula to calculate the standard deviation for the sample. That is,

$σ_{x} = \frac{σ}{\sqrt{n}}$

From the above equation,

$σ_{x}$ is the standard deviation for the sample

$σ$ is the standard deviation

$n$ is the sample size

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