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