PTC is a substance that has a strong bitter taste for some people and is tastele

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 76% 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 answers up to the nearest person.) starting with the 76% estimate, how large a sample must you collect in order to estimate the proportion of PTC tasters within plus minus 0.02 with 90% confidence? N = people Estimate the sample size required if you made no assumptions about the value of the proportion who could taste PTC. N = people

Explanation / Answer

Answer:

a).

Sample size calculation

p=0.76

For 90%, z=1.645

d=0.02

Sample size = (z2*p*(1-p))/d2

= (1.6452*0.76*0.24)/0.022

=1233.9

The sample size required=1234

b).

p=0.5( assuming)

For 90%, z=1.645

d=0.02

Sample size = (z2*p*(1-p))/d2

= (1.6452*0.5*0.5)/0.022

=1691.2

The sample size required=1692

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