Question

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 $16,642 . Assume that the standard deviation is $2,812 . 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 $202 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 +/- 202 of ranges from_____ for a sample of size 30 to_____ for a sample of size 400.

Answer 1

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 $202 of the population mean for each of the following sample sizes: 30,50, 100, 400?

Answer:

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 +/- 202 of ranges from 0.1530 for a sample of size 30 to 0.4246 for a sample of size 400.