For the year 2010, 33% of taxpayers with adjusted gross incomes between $30,000

Question

For the year 2010, 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return (The Wall Street Journal, October 25, 2012). The mean amount of deductions for this population of taxpayers was 26, $16.642. Assume the standard deviation is $2400. 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 a. each of the following sample sizes: 30, 50, 100, and 400? b. What is the advantage of a larger sample size when attempting to estimate the popu- lation mean?

Explanation / Answer

a)

(i)

(ii)

(iii)

(iv)

b) advantage of having large sample is that there is higher probability tht sample will remain with in a smaller margin of error from population mean,

for normal distribution z score =(X-)/ here mean=       = 16642 std deviation   == 2400.0000

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