Question 1172983: For the year 2010, 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000
itemized deductions on their federal income tax return (The Wall Street Journal, October 25, 2012).
The mean amount of deductions for this population of taxpayers was $16,642. Assume the standard
deviation is 𝜎 = $2400.
3.1. 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: 30, 50, 100, and 400?
3.2. What is the advantage of a larger sample size when attempting to estimate the population mean?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z < (x-mean)/sd/sqrt(n) and z> (-200*sqrt(30)/2400)
z < 200*sqrt(30)/2400
-0.46 < z < 0.46
probability is 0.3545
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with sample size of 50
it is
probability is 0.4448
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with sample size of 100
it is < abs (200*10/2400) or -0.83 < z < 0.83
probability is 0.5935
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with n=400
-1.67 < z < 1.67
probability is 0.9051
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The larger the sample size, the more likely the estimate of the population mean will be within a fixed interval.
Confidence intervals will be narrower. The sampling distribution of the sample mean over different sample sizes will become sharper, less variable, the greater the sample size.
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