# Hypothesis Testing About Americans Estimating Foreign Aid In Federal Budget

Question

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. 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. 2. You need not calculate a new Z statistic to answer this question.

Summary

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.

Total Word Count 199

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