Can you taste PTC? PTC is a substance that has a strong bitter taste for some pe

Question

Can you taste PTC?

PTC is a substance that has a strong bitter taste for some peopleand is tasteless for others. The ability to taste PTC isinherited. About 75% of Italians can taste PTC, forexample. You want to estimate the proportion of Americanswith at least one Italian grandparent who can taste PTC.

a)Starting with the 75% estimate for Italians, how large a samplemust you collect in order to estmiate the proportion of PTC tasterswithin + or -0.04 with 90% confidence?

b) Estimate the sample size required if you made no aaumptions about the value of proportions who could tatse PTC. How much has the required sample size changed?

Explanation / Answer

a.

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)

Z a/2 at 0.1 is = 1.645

Sample Proportion = 0.75

ME = 0.04

n = ( 1.645 / 0.04 )^2 * 0.75*0.25

= 317.112305 ~ 318

b.

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)

Z a/2 at 0.1 is = 1.645

Sample Proportion = 0.5

ME = 0.04

n = ( 1.645 / 0.04 )^2 * 0.5*0.5

= 422.8164 ~ 423

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