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Suppose that the ages of members in a large billiards league have a known standard deviation of σ = 12 σ=12sigma, equals, 12 years. Hernando plans on taking a random sample of n nn members from this population to make a 95 % 95%95, percent confidence interval for the mean age in the league. He wants the margin of error to be no more than 5 55 years. Which of these is the smallest approximate sample size required to obtain the desired margin of error?

User Jasim
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1 Answer

1 vote

Answer:


n\geq 23

Explanation:

-For a known standard deviation, the sample size for a desired margin of error is calculated using the formula:


n\geq ((z\sigma)/(ME))^2

Where:


  • \sigma is the standard deviation

  • ME is the desired margin of error.

We substitute our given values to calculate the sample size:


n\geq ((z\sigma)/(ME))^2\\\\\geq ((1.96* 12)/(5))^2\\\\\geq 22.13\approx23

Hence, the smallest desired sample size is 23

User Celso Wellington
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