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 $17,696. Assume that the standard deviation is o = $2,256. 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 $229 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? 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 ( increases A the probability that the sample mean will be within a specified distance of the population mean. In the for a sample of size 30 to for a sample of automobile insurance example, the probability of being within +229 of u ranges from size 400.

Answer 1

	Answers
n=30	0.4218
n=50	0.5271
n=100	0.6899
n=400	0.9577

A large sample increase the probability that the sample mean will be within a specified distance of the population mean u ranges from 0.4218 for a sample size 30 to 0.9577 for a sample of  400.