Question

A researcher wishes to estimate, with 95% 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 34% of the respondents said they think their president can control the price of gasoline.

Answer #1

Solution :

Given that,

margin of error = E = 0.02

Z_{/2}
= 1.96

(a)

= 0.5

1 - = 0.5

sample size = n = (Z_{ / 2} / E)^{2} *
* (1 - )

= (1.96 / 0.02)^{2} * 0.5 * 0.5

= 2401

sample size = n = 2401

(b)

= 0.34

1 - = 0.66

sample size = n = (Z_{ / 2} / E)^{2} *
* (1 - )

= (1.96 / 0.02)^{2} * 0.34 * 0.66

= 2401

sample size = n = 2156

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