Find the sample size needed to estimate the percentage of residents of one regio

Question

Find the sample size needed to estimate the percentage of residents of one region of a country who are left-handed. Use a margin of error of five percentage points and use a confidence level of 95%. Complete parts (a) through (c) below. a. Assume that p and q are unknown The sample size needed is Round up to the nearest whole number as needed.) b. Assume that based on prior studies, about 12% of residents of the region are left-handed. The sample size needed is Round up to the nearest whole number as needed.) c. How do the results from parts (a) and (b) change if the entire country is used instead of the one region of that country? If the entire country is used instead of the one region of that country, the result from part (a) Y and the result from part (b)

Explanation / Answer

SolutionA:

E=5%=0.05

Z alpha/2 for 95%=1.96

p^ and q^are unknown

so p^=1/2=0.5

and q^=1-p^=1-0.5=0.5

n=p^*q^*(zalpha/2/E)^2

=0.5*0.5*(1.96/0.05)^2

=384.16

=384

sample size needed=384

Solutionb:

p^=12%=0.12

q^=1-0.12=0.88

n=0.12*0.88*(1.96/0.05)^2

n=162.26

sample size needed=162

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