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School vouchers A national opinion poll found that 44% of all American adults agree that
Chapter 8, Problem 44(choose chapter or problem)
School vouchers A national opinion poll found that 44% of all American adults agree that parents should be given vouchers that are good for education at any public or private school of their choice. The result was based on a small sample.
(a) How large an SRS is required to obtain a margin of error of 0.03 (that is, \(\pm3 \%\)) in a 99% confidence interval? Answer this question using the previous poll’s result as the guessed value for \(\hat{p}\).
(b) Answer the question in part (a) again, but this time use the conservative guess \(\hat{p}=0.5\). By how much do the two sample sizes differ?
Questions & Answers
QUESTION:
School vouchers A national opinion poll found that 44% of all American adults agree that parents should be given vouchers that are good for education at any public or private school of their choice. The result was based on a small sample.
(a) How large an SRS is required to obtain a margin of error of 0.03 (that is, \(\pm3 \%\)) in a 99% confidence interval? Answer this question using the previous poll’s result as the guessed value for \(\hat{p}\).
(b) Answer the question in part (a) again, but this time use the conservative guess \(\hat{p}=0.5\). By how much do the two sample sizes differ?
ANSWER:Step 1 of 4
a) For a 99% confidence interval, we catch the central 99% and leave out the 1%. Therefore, on each tail we leave out 0.5%. So the desired critical value 
Using table showing standard normal probabilities, we find the 
The closest value is z=2.576
So the critical value is 