The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between $30,000 and...

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Statistics

The Wall Street Journal reported that 33% of taxpayerswith adjusted gross incomes between $30,000 and $60,000 itemizeddeductions on their federal income tax return. The mean amount ofdeductions for this population of taxpayers was $16,928 . Assumethat the standard deviation is $2,903.
(a) What is the probability that a sample of taxpayers from thisincome group who have itemized deductions will show a sample meanwithin $151 of the population mean for each of the following samplesizes: 30, 50, 100, and 400? Round your answers to fourdecimals.
(b) What is the advantage of a larger sample size whenattempting to estimate the population mean? Round your answers tofour decimals.
A larger sample increases the probability that the sample meanwill be within a specified distance of the population mean. In theautomobile insurance example, the probability of being within(plus/minus) $151 of m ranges from (blank) for a sample of size 30to (blank) for a sample of size 400.

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3.5 Ratings (578 Votes)

Let X be the amount of deductions for this population oftaxpayersX has a mean andstandard deviation a Let representthe sample mean amount of deductions for a sample of size nif n is greater than 30 or we know the population standarddeviation the central limit theorem says that has anormal distribution with mean and standard deviation or called standard error of meanthe probability that a sample of taxpayers See Answer

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