Question

 

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

σ = $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, 150, and 500? (Round your answers to four decimal places.)

sample size n = 20sample size n = 60sample size n = 150sample size n = 500

(b)

What is the advantage of a larger sample size when attempting to estimate the population mean?

A larger sample increases the probability that the sample mean will be within a specified distance of the population mean.A larger sample lowers the population standard deviation.    A larger sample increases the probability that the sample mean will be a specified distance away from the population mean.A larger sample has a standard error that is closer to the population standard deviation.

Answer 1

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Answer:

a)

For n = 150, P(ABS(Z) < 1.02062) = 2P(00.6926

b)

A larger sample size when attempting to estimate the population means that the standard deviation will be lower which will be useful in accurate confidence intervals. Hence Option B