Question

# A researcher wishes to​ estimate, with 99​% ​confidence, the population proportion of adults who think the...

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

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 * 0.32 * 0.68 / 0.022

= 3609.28

Minimum sample size = 3609

c)

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

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