If the sample size n is doubled, by how much is the length

Chapter 8, Problem 20E

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QUESTION:

If the sample size n is doubled, by how much is the length of the CI on \(\mu\) in Equation 8-5 reduced? What happens to the length of the interval if the sample size is increased by a factor of four?

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QUESTION:

If the sample size n is doubled, by how much is the length of the CI on \(\mu\) in Equation 8-5 reduced? What happens to the length of the interval if the sample size is increased by a factor of four?

ANSWER:

Step 1 of 3

For a sample mean, , of a random sample of size n from a normal population with known variance , a  Confidence Interval on  is given by (Equation 8-5),

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