In the following passage, identifying sample, population, attribute of interest, and the extent to which the claims involved are knowable. Consider carefully the size and diversification of the sample and the extent to which the population differs or may differ from the sample; remember, what's important is that the sample be representative. Do you find any flaw in our professor's reasoning about the usefulness of the survey for her own purposes? Should she believe that the more people who have home offices, the more likely her own will escape attention from the IRS?A college professor converted one room of her house into a home office and intended to deduct her expenses on her federal income tax return. She wondered how many other college faculty had done the same, thinking that the more

Question

who deducted home offices, the less likely her own return would be noticed by the IRS and hence the less likely she would be audited. So she decided to do her own informal survey of her colleagues to see how many of them had home offices. She sent out a questionnaire of three questions to all 1,200 instructors at her campus, and she received 950 responses. (Her promise to share the results of the survey apparently motivated faculty to respond.)As it turned out, 32 percent of her respondents answered yes to the question, "Do you maintain an office at home?" Half of these also answered yes to the question, "Do you deduct your home office expenses on your federal income tax return?" And 24 percent of the entire group of respondents answered yes to the question, "Is your campus office adequate?"

What will be an ideal response?

Answer 1

This is not a question about the criteria for evaluating statistical generalizations, but rather about the assumption that motivated the study. It does us no good to produce studies to answer questions if they are the wrong questions to begin with. In this case, it may be that the IRS will turn more attention to home office deductions if there are enough of them to constitute a large total of deductions. Our professor has done a good job of answering some questions (about office space, about the number of home offices maintained by her colleagues and at other campuses similar to hers) but she had best be careful not to let her enthusiasm at having produced some reliable figures rub off on her initial assumption; such a mistake could be costly at tax time.