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 their country can control the price of gasoline. Her estimate must be accurate within 4% of the true proportion.

a) No preliminary estimate is available. Find the minimum sample size needed. n = ?

b) Find the minimum sample size needed, using a prior study that found that 44% of the respondents said they think their president can control the price of gasoline. n = ?

c) Compare the results from parts (a) and (b).

Explanation / Answer

n both cases, the margin of error is E = 0.04. The critical value is approximately z = 2.575 (found using a table or calculator)


A) "no preliminary estimate is available" so assume that p = 0.5

n = p(1-p)(z/E)^2

n = 0.5(1-0.5)(2.575/0.04)^2

n = 1036.03

n = 1036

Notice how I rounded up to the nearest whole number.

Min sample size needed is 1036


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b) Now we are told that p = 0.44

n = p(1-p)(z/E)^2

n = 0.44(1-0.44)(2.575/0.04)^2

n = 1021.1162

n = 1022

Again, round up to the nearest integer.

Min sample size needed is 1022

There isn't much difference between the two min sample sizes: 1036 from part a) and 1022 from part b)

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