Q.17 - The Practice of Statistics for AP

Question

IRS audits 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 each state varies from over 15 million in California to about $240,000$ in Wyoming.

(a) Will the sampling variability of the sample proportion change from state to state if an SRS of $2000$ tax returns is selected in each state? Explain your answer.

(b) Will the sampling variability of the sample proportion change from state to state if an SRS of $1\%$of all tax returns is selected in each state? Explain your answer

Step-by-Step Solution

Answer

a). Yes,  the sampling variability will differ from state to state.

b). Yes,  the sampling variability will differ from state to state. 

Part (a) Step 1: Given Information

The total number of tax returns in each state varies from over $15$ million in California to about $240,000$ in Wyoming. 

Part (a) Step 2: Explanation

Yes, the sampling variability will differ from state to state, because some states will have more variability in the tax returns (more extremely low and more extremely high tax returns) as other states.

Part (b) Step 1: Given Information

The total number of tax returns in each state varies from over $15$ million in California to about $240,000$ in Wyoming. 

Part (b) Step 2: Explanation

We take a simple random sample of $2000$ tax returns from each state.

The state of California has a larger population than the state of Wyoming.

If the SRS of $2000$ students is a larger part of the population, then there will be less sampling variability for the state and thus Wyoming will have less sampling variability than California.