Question

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 78% of Italians can taste PTC, for example. You want to estimate the proportion of Americans with at least one Italian grandparent who can taste PTC. How large a sample must you collect in order to estimate the proportion of PTC tasters to within ±0.04 with 90% confidence?

n=?

Answer 1

Solution :

Given that,

= 78% = 0.78

1 - = 1 - 0.78 = 0.22

margin of error = E = 0.04

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.01 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.645 / 0.04)² * 0.78 * 0.22

= 290.2 = 290

sample size = 290