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Chapter 8: Q 50. (page 523)

Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75%of Italians can taste PTC, for example. You want to estimate the proportion of Americans who have at least one Italian grandparent and who can taste PTC.

a. How large a sample must you test to estimate the proportion of PTC tasters within 0.04with 90%confidence? Answer this question using the 75%estimate 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=318

b. Sample size increases by105.

Step by step solution

01

Given Information

It is given that E=0.04,p^=0.50

1-α=0.90, using tableza/2=1.645

02

Calculating Sample Size

It is calculated as: p^known:n=za/22p^q^E2

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

and p^unknown:n=za/220.25E2

As p^is known, sample size

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

=1.6452×0.75(1-0.75)0.042

n=318

03

Increase in Sample Size

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

=1.6452×0.50(1-0.50)0.042

=423

Difference between two sizes, 423-318

=105

Sample size increases by105

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