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According to the Current Population Report of the United States census, 26.7% of people aged 65 and older have earned a bachelor's degree or higher. Suppose that Nancy works for the city of Peoria, AZ. City officials have asked her to estimate the proportion of people aged 65 and older in Peoria who have earned a bachelor's degree or higher. They have requested that her estimate have confidence level of 90% and a margin of error of 3%, or 0.03. Determine the sample size n needed for the 90% confidence interval to be no more than 0.03.

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Answer:

At least 585 people aged 65 and older is needed to be surveyed for the 90% confidence level and 3% margin of error.

Step-by-step explanation:

The following formula can be used to compute the minimum sample size required to estimate the population proportion  within the required margin of error:

n≥ p×(1-p) × [tex](\frac{z}{ME} )^2[/tex] where

  • n is the sample size
  • p is the proportion of people aged 65 and older have earned a bachelor's degree or higher (26.7% or 0.267)
  • z is the corresponding z-score for 90% confidence level (1.64)
  • ME is the expected margin of error in the estimation (0.03)

then n≥ 0.267×0.733 × [tex](\frac{1.64}{0.03} )^2[/tex]≈584.87

Then n should be at least 585

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