Question

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who support labeling legislation for genetically modified organisms (GMOs). Her estimate must be accurate within 5% of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 66% of the respondents said they support labeling legislation for GMOs. (c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available? nequals nothing (Round up to the nearest whole number as needed.)

Answer #1

a) From standard normal tables, we have:

P( -1.96 < Z < 1.96) = 0.95

The margin of error here is given to be 0.05. It is computed here as:

As we dont have any prior proportion estimate, we use p = 0.5 to get a conservative sample size here as:

**therefore 385 is the required sample size
here.**

b) For a prior proportion value of p = 0.66, we get the sample size here as:

**therefore 345 is the required sample size
here.**

c) Comparing the results from the above 2 parts, clearly as we have a prior proportion estimate, the required sample size decreases here.

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6.3.17
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