The Internal Revenue Service plans to examine an SRS of individual federal incom

Question

The Internal Revenue Service plans to examine an SRS of individual federal income tax returns from each state. One variable of interest is the proportion of returns claiming itemized deductions. The total number of tax returns in a state varies from more than 15 million in California to fewer than 250,000 in Wyoming.

a) Will the margin of error for estimating the population proportion change from state to state if an SRS of 2,000 tax returns is selected in each state?

b) Will the margin of error change from state to state if an SRS of 1% of all tax returns is selected in each state?

Explanation / Answer

a) Will the margin of error for estimating the population proportion change from state to state if an SRS of 2,000 tax returns is selected in each state? Since the smallest number of total tax returns (i.e., the smallest population) is still more than 100 times the sample size, the variability will be (approximately) the same for all states. b) Will the margin of error change from state to state if an SRS of 1% of all tax returns is selected in each state? Yes, it will change—the sample taken from Wyoming will be about the same size, but the sample in, e.g., California will be considerably larger, and therefore the variability will decrease. please, rate! thank you.

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