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 $17,743. Assume that the standard deviation is σ = $2,581. 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 $227 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- Select your answer-, 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 +/-227 of M ranges from ( ) for a sample of size 30 to ( ) for a sample of size 400.

Answer 1