Question

PTC is a substance that has a strong bitter tatse for some people and is tasteless for others. The ability to taste PTC is inherited. About 77% of people from a certain country can taste PTC, for example. You want to estimate the proportion of people with at least one grandparent from this country who can taste PTC. (round your answer to the nearest person).

(a) Starting with the 77% estimate, how large a sample must you collect in order to estimate the proportion of PTC tasters within plus or minus 0.01 with 90% confidence?

(b) Estimate the sample size required if you made no assumptions about the value of the proportion who could taste PTC.

(c) How much has the required sample size changed? Decreased or increased by more or less than a hundred or no change

Answer 1

Ans:

a)Prior estimate=0.77

Margin of error=0.01

z=1.645

Sample size required,n=1.645^2*0.77*(1-0.77)/0.01^2=4792

b)

When no prior estimate,then p=0.5

Sample size required,n=1.645^2*0.5*(1-0.5)/0.01^2=6765

c)

Increased by more than a hundred