Question 7.91

image 61. The Internal Revenue Service (IRS) plans to examine an SRS of individual income tax returns from each state that were filed electronically. One variable of interest is the proportion of returns that were filed by a tax practitioner rather than by an individual taxpayer. The total number of e-filed tax returns in a state varies from 4.9 million in California to 97,000 in Vermont.

  1. Will the margin of error for estimating the proportion change from state to state if an SRS of 1000 e-filed returns is selected in each state? Explain your answer.
  2. Will the margin of error change from state to state if an SRS of 1% of all e-filed returns is selected in each state? Explain your answer.

61.

(a) No. The number of e-filed returns in all states is much larger than the sample size. When this is true, the margin of error depends only on the size of the sample, not on the size of the population.

(b) Yes. The sample sizes vary from 970 to 49,000, so the margins of error will also vary.