Question

# A researcher wishes to​ estimate, with 95​% ​confidence, the population proportion of adults who support labeling...

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.)

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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