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We are interested in conducting a study in order to determine what percentage of voters of a state would vote for the incumbent governor. What is the minimum size sample needed to estimate the population proportion with a margin of error of +/-0. 06 at 95% confidence?.

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Using the appropriate sample size formula, the minimum number of samples required is 267

Using the relation :

  • N = [(Z² × pq) / e²]
  • e = Error Margin = 0.06² = 0.0036
  • p = 0.5
  • q = 1 - 0.5 = 0.5
  • Zcritical at 95% = 1.96

Substituting the values into the equation :

N = [(1.96² × (0.5 × 0.5)) / 0.0036]

N = (0.9604 / 0.0036)

N = 266.777

N = 267

Hence, the minimum number of samples required is 267

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