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 $16,202.
Assume that the standard deviation is a = $2617. Use z-table.
σ=
a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample
mean within $213 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 increases
the probability that the sample mean will be within a specified distance of the population
mean. In this instance, the probability of being within +213 of μ ranges from
for a sample of size 30 to
for a
sample of size 400.
