minimum sample size necessary

Hi, I was wondering if this solution is correct

A researcher wants to estimate, with 95% confidence, the proportion of people who own a car. A previous study shows that 30% of those interviewed had a car. The researcher wants to be accurate within 1% of the true proportion. Find the minimum sample size necessary.

1.96 [(0.30*0.70)/rootn]=0.01

n=2213.76

so he should take 2213 people

thanks

fx'ns said:

Hi, I was wondering if this solution is correct

A researcher wants to estimate, with 95% confidence, the proportion of people who own a car.

A previous study shows that 30% of those interviewed had a car.

The researcher wants to be accurate within 1% of the true proportion.

Find the minimum sample size necessary.

1.96 [(0.30*0.70)/rootn]=0.01

n=2213.76

so he should take 2213 people

thanks

Click to expand...

fx'ns, here is some information to help you try the problem again:


"Formula For Calculating A Sample For Proportions

For populations that are large, Cochran (1963:75) developed the Equation 1 to yield a representative sample for proportions.

\(\displaystyle n_0 \ = \ \dfrac{Z^2pq}{e^2}\)

Equation 1. Which is valid where n₀ is the sample size, Z² is the abscissa of the normal curve that cuts off an area α at the tails
(1 - α equals the desired confidence level, e.g., 95%)¹, e is the desired level of precision, p is the estimated proportion
of an attribute that is present in the population, and q is 1-p. The value for Z is found in statistical tables which contain
the area under the normal curve."


Source: http://edis.ifas.ufl.edu/pd006

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And, no matter what the fractional part you get after initially computing the sample size,
you *always round up* to the next integer when you report the minimum sample size.