You may need to use the appropriate appendix table or technology to answer this question. 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 follow sample sizes: 20, 50, 100, and 500? (Round your answers to four decimal places.) sample size n = 20 sample size n = 50 sample size n = 100 sample size n = 500 (b) What is the advantage of a larger sample size when attempting to estimate the population mean? O A larger sample increases the probability that the sample mean will be within a specified distance of the population mean. O A larger sample increases the probability that the sample mean will be a specified distance away from the population mean. O A larger sample has a standard error that is closer to the population standard deviation. O A larger sample lowers the population standard deviation.

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You may need to use the appropriate appendix table or technology to answer this question.
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, 50, 100, and 500? (Round your answers to four decimal places.)
sample size n =
20
sample size n = 50
sample sizen = 100
sample size n = 500
(b) What is the advantage of a larger sample size when attempting to estimate the population mean?
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 has a standard error that is closer to the population standard deviation.
A larger sample lowers the population standard deviation.
Transcribed Image Text:You may need to use the appropriate appendix table or technology to answer this question. 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, 50, 100, and 500? (Round your answers to four decimal places.) sample size n = 20 sample size n = 50 sample sizen = 100 sample size n = 500 (b) What is the advantage of a larger sample size when attempting to estimate the population mean? 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 has a standard error that is closer to the population standard deviation. A larger sample lowers the population standard deviation.
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