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 and depends on a single gene that codes for a taste receptor on the tongue. Interestingly, although the PTC molecule is not found in nature, the ability to taste it correlates strongly with the ability to taste other naturally occurring bitter substances, many of which are toxins. About 75% of Italians can taste PTC. You want to estimate the proportion of Americans with at least one Italian grandparent who can taste PTC.

(a) Starting with the 75% estimate for Italians, how large a sample must you collect in order to estimate the proportion of PTC tasters within ±0.11 with 95% confidence? (Enter your answer as a whole number.)

n=

(b) Estimate the sample size required if you made no assumptions about the value of the proportion who could taste PTC. (Enter your answer as a whole number.)

n=

Answer 1

Solution :

Given that,

margin of error = E = 0.11

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

(a)

= 0.75

1 - = 1 - 0.75 = 0.25  

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

= (1.96 / 0.11)² * 0.75 * 0.25

= 59.52

sample size = 60

(b)

= 0.5

1 - = 1 - 0.5 = 0.5

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

= (1.96 / 0.11)² * 0.5 * 0.5

= 79.37

sample size = 80