Question

The Wall Street Journal reported that of taxpayers with adjusted gross incomes between and itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was . Assume that the standard deviation is . 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 of the population mean for each of the following sample sizes: , , , and ? Round your answers to four decimals. 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 the automobile insurance example, the probability of being within of ranges from for a sample of size to for a sample of size .

Answer 1

Assuming

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 $15,468 . Assume that the standard deviation is $2,839 . 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 of the $183 of population mean for each of the following sample sizes: 30,50 ,100 ,400 and ? Round your answers to four decimals.

n=30 ______

n=50 _______

n=100 ______

n=400 _______

b. What is the advantage of a larger sample size (either increases or decreases) 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 the automobile insurance example, the probability of being within +/- 183 of ranges from_____ for a sample of size 30 to_____ for a sample of size 400.

Solution