Favorites a) AirDrop Recents Screen Shot 2018-0... 17.25 PM Screen Shot Screen S

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Favorites a) AirDrop Recents Screen Shot 2018-0... 17.25 PM Screen Shot Screen Shot Screen Shot 2018-0.. 17.11 PM 2018-0.. 16.06 PM 2018-0.. 15.46 PM 2018-0... 15.29 PM iCloud Drive Screen Shot Applications Deskto Screen Shot 2018-03-01 at 6.17.25 PM Open with Preview 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 26. $16.642. Assume the standard deviation is = $2400. 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 a. Tag each of the following sample sizes: 30, 50, 100, and 400? b. What is the advantage of a larger sample size when attempting to estimate the popu- lation mean?

Explanation / Answer

a)

for sample size ; n=30;

for sample size ; n=50;

for sample size ; n=100;

  for sample size ; n=400;

b) as in part a) we can see that as sample size is increased probability of finding the mean with in a interval increases; whcih mean increasing the sample size increases the precision of estimated mean due to lowering its standard deviation.

for normal distribution z score =(X-)/ here mean=       = 16642.000 std deviation   == 2400.0000 sample size       =n= 30 std error=x=/n= 438.1780

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