The Gallup Poll asked a probability sample of 2500 U.S. adults whether they used a credit...

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The Gallup Poll asked a probability sample of 2500 U.S. adults whether they used a credit...

The Gallup Poll asked a probability sample of 2500 U.S. adults whether they used a credit card to pay for groceries that week. Suppose that 25% of the adult population did. We would like to know the probability that an SRS of size 2500 would come within plus or minus 2 percentage points of this true value.
1. If p-hat is the proportion of the sample who did use a credit card to pay for groceries, what is the mean of p-hat? (2 points)
2. What is the standard deviation of p-hat? (2 points)
3. Explain why you can use the formula for the standard deviation of p-hat in this setting. (2 points)
4. Check that you can use the normal approximation for the distribution of p-hat.(2 points)
5. Find the probability that p-hat takes a value between 0.23 and 0.27. (4 points)

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Answer 1

Answer #1

-Given no-of ample s3500 A) Mean of phat- 0,as PCi-P) 2500 2SD0 000866 02SG 0 0 00866 SE () and gauiats VPtr-PI ewor p.haf is knn as tho standed Fronn Obove we Can Cee that both valuar wra great es dhan 1o ,So cve Can use the nomalabudion, オ1 て(x:0,a 3) :-23, r(-231くスく2.31): D19798

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The Gallup Poll asked a probability sample of 2500 U.S. adults whether they used a credit...

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