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Last modified: January 26, 2018

Sample Size Determination ------------------------- The error arising due to drawing inferences about the population on the basis of sampling is termed as sampling error. The margin of error is the maximum error expected in stating, at a level of confidence, an interval within which the population parameter is supposed to lie. Margin of Error, MOE = Zα/2σ/√n _ _ Confidence interval: x - MOE < μ < x + MOE _ _ Take x - MOE = μ ∴ x - μ = MOE Or, for a proportion: MOE = Zα/2√(pq/n) Rearranging, _ n = (Zα/2σ/x - μ)2 = (Zα/2σ/MOE)2 Or, for a proportion: n = (Zα/2/MOE)2pq using σ = √(pq/n) In the case where p is unknown, a value of 0.5 is used to provide a conservative estimate of the sample size. The approximated MOE formula is then: MOE = ±1.96√(0.5(1 - 0.5)/n) = ±1.96√(0.25/n) = ±1.96*0.5√(1/n) ~ ±1/√n Ex. In a random survey of 1,000 Floridians, 43% of the respondents liked Ford pickups over Chevy pickups and 52% liked Chevy pickups over Ford pickups. 5% had no preference. First, set n = 1,000 and p = 0.43. Then ±1.96√((0.43*0.52)/1000) = ±0.0293 This means that if you perform the same survey 100 more times, then 95% of the time the number of people who liked Ford more than Chevy should be between 40.1% and 45.9%.