In a simple random sample of 144 Americans, respondents were asked to estimate the share of the U.S. federal budget devoted to foreign aid. The average of the responses was 24.8%, with a standard deviation in responses of 12%. The actual share of the U.S. federal budget devoted to foreign aid is 0.8%1.
(a) Test the hypothesis that Americans, on average, correctly estimate the share of the federal budget devoted to foreign aid. Report the Z-statistic. Compare the p-value to 1%.
(b) Did you have to bootstrap the standard error? Why or why not? (Hint: think about the box model underlying this sample.)
(c) Suppose the same average were observed in a poll of 30 Americans. Would you expect the p-value to be bigger or smaller than the answer from part (A) above?2
- 1. These numbers have been modified slightly to make the arithmetic easy and round. But only slightly: this is pretty close to the discrepancy between beliefs about the U.S. foreign aid budget and the actual foreign aid budget.
- 2. You need not calculate a new Z statistic to answer this question.
The question belongs to Statistics and it discusses about testing a hypothesis that Americans can correctly estimate the share of federal budget devoted to foreign aid.
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