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Hint(s) Check my work The Wall Street Journal reported 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 $16,810. Assume that the standard deviation is a = $2975. Use z-table. a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $228 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals. n = 30 n = 50 n = 100 n = 400 b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals. A larger sample Select your answer - the probability that the sample mean will be within a specified distance of the population mean. In this instance, the for a sample of size 30 to for a sample of size 400. probability of being within +228 of μ ranges from

Hint(s) Check my work The Wall Street Journal reported 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 $16,810. Assume that the standard deviation is a = $2975. Use z-table. a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $228 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals. n = 30 n = 50 n = 100 n = 400 b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals. A larger sample Select your answer - the probability that the sample mean will be within a specified distance of the population mean. In this instance, the for a sample of size 30 to for a sample of size 400. probability of being within +228 of μ ranges from

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**The Wall Street Journal** reported 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 $16,810. Assume that the standard deviation is \( \sigma = \$2975 \). Use the z-table. **a.** What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $228 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals. - \( n = 30 \) - \( n = 50 \) - \( n = 100 \) - \( n = 400 \) **b.** What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals. A larger sample ___ the probability that the sample mean will be within a specified distance of the population mean. In this instance, the probability of being within ±228 of \( \mu \) ranges from ___ for a sample of size 30 to ___ for a sample of size 400.
Transcribed Image Text:**The Wall Street Journal** reported 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 $16,810. Assume that the standard deviation is \( \sigma = \$2975 \). Use the z-table. **a.** What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $228 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals. - \( n = 30 \) - \( n = 50 \) - \( n = 100 \) - \( n = 400 \) **b.** What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals. A larger sample ___ the probability that the sample mean will be within a specified distance of the population mean. In this instance, the probability of being within ±228 of \( \mu \) ranges from ___ for a sample of size 30 to ___ for a sample of size 400.
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