The Wall Street Journal reports 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 the standard deviation is o- = $2,400. (a) 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 each of the following sample sizes: 20, 60, 100, and 400? (Round your answers to four decimal places.) sample size n = 20 sample size n = 60 sample size n = 100 sample size n = 400 (b) What is the advantage of a larger sample size when attempting to estimate the population mean? if) A larger sample lowers the population standard deviation. if” A larger sample has a standard error that is closer to the population standard deviation. (5. A larger sample increases the probability that the sample mean will be a specified distance away from thepopulation mean. ‘7’; A larger sample increases the probability that the sample mean will be within a speci?ed distance of the population mean. … Show moreMathStatistics and Probability STAT 2500
