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 σ = $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: 30, 50, 100, and 500? (Round your answers to four decimal places.) sample size n = 30sample size n = 50sample size n = 100sample size n = 500 (b) What is the advantage of a larger sample size when attempting to estimate the population mean? A larger sample lowers the population standard deviation.A larger sample increases the probability that the sample mean will be a specified distance away from 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.
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 σ = $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: 30, 50, 100, and 500? (Round your answers to four decimal places.) sample size n = 30sample size n = 50sample size n = 100sample size n = 500 (b) What is the advantage of a larger sample size when attempting to estimate the population mean? A larger sample lowers the population standard deviation.A larger sample increases the probability that the sample mean will be a specified distance away from 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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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
σ = $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: 30, 50, 100, and 500? (Round your answers to four decimal places.)
(b)
What is the advantage of a larger sample size when attempting to estimate the population mean?
A larger sample lowers the population standard deviation.A larger sample increases the probability that the sample mean will be a specified distance away from 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.
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