Question

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?

Answer 1

Answer:

$n\geq 23$

Step-by-step explanation:

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

$n\geq (\frac{z\sigma}{ME})^2$

Where:

• $\sigma$ is the standard deviation
• $ME$ is the desired margin of error.

We substitute our given values to calculate the sample size:

$n\geq (\frac{z\sigma}{ME})^2\\\\\geq (\frac{1.96\times 12}{5})^2\\\\\geq 22.13\approx23$

Hence, the smallest desired sample size is 23