Question

# The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between \$30,000 and...

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,

60,

150, and

300? (Round your answers to four decimal places.) sample size n = 30 sample size n = 60 sample size n = 150 sample size n = 300

(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. (b) A larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

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