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Chapter 8: Q 49. (page 523)

School vouchers A small pilot study estimated 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.

a. How large a random sample is required to obtain a margin of error of at most 0.03with 99%confidence? Answer this question using the pilot study’s result as the guessed value for p^

b. Answer the question in part (a) again, but this time use the conservative guessp^=0.5. By how much do the two sample sizes differ?

Short Answer

Expert verified

a. n=1816

b. Increase in sample size is26.

Step by step solution

01

Given Information

It is given that E=0.03

p^=44%=0.44

02

Calculation of n

Sample size is p^known:n=za/22p^q^E2

=za/22p^(1-p^)E2

and p^unknown:n=za/220.25E2

Now for 1-α=0.99, using table za/2=2.575

Hence, n=zα/22p^(1-p^)E2

=2.5752×0.44(1-0.44)0.032

n=1816

03

Increase in Sample Size

Asp^is known, hence

n=za/22p^(1-p^)E2

=2.5752×0.50(1-0.50)0.032

n=1842

Difference between two sizes is 1842-1816=26

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