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 2% 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 40% of the respondents said they think their president can control the price of gasoline. c) Compare the results from parts (a) and (b).

Explanation / Answer

a)

When proportion is not specified, p = 0.50

Sample size n = Z2 P ( 1 - P) / E2

Where E is error = 0.02

n = 2.57582 * 0.5 * 0.5 / 0.022

= 4146.72

Minimum sample size = 4147

b)

Sample size n = Z2 P ( 1 - P) / E2

n = 2.57582 * 0.4 * 0.6 / 0.022

= 3980.85

Minimum sample size = 3981

c)

Sample size required is lower when proportion is given rather than proportion is unknown.

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