a researcher wishes to estimate, with 99% confidence, the population proportion

Question

a researcher wishes to estimate, with 99% confidence, the population proportion of adults who think the president of ther country can control the price of gasoline. Her estimate must be accurate within 5% of the true proportion.

a) NO preliminary estimate is available. Find the minium sample size needed.

b) FInd the minimum samples size needed, using a prior study that found that 20% of the respondents said they think their preseident can control the price of gasoline.

c) COmpare the results from parts (a) and (b)

WHat is the minimum samples size needed assuming that no prior information is available?

n= (round to the nearest whole number as needed)

Explanation / Answer

A researcher wishes to estimate, with 99% confidence, the population proportion of adults who think the president of the country can control the price of gasoline. Her estimate must be accurate within 5% of the true proportion.

For 99%, z=2.576

d=0.05

we are assuming p=0.5,

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

= (2.5762*0.5*0.5)/0.052

=663.57

The sample size required= 664

b) FInd the minimum samples size needed, using a prior study that found that 20% of the respondents said they think their preseident can control the price of gasoline.

When p=0.2,

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

= (2.5762*0.2*0.8)/0.052

=424.68

The sample size required= 425

c) COmpare the results from parts (a) and (b)

when we know prior estimate of p, the sample size required is small compared to prior estimate not available.

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