Solved: A random sample has been taken from a normal

Chapter 8, Problem 6E

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QUESTION:

A random sample has been taken from a normal distribution and the following confidence intervals constructed using the same data: (37.53, 49.87) and (35.59, 51.81)

(a) What is the value of the sample mean?

(b) One of these intervals is a 99% CI and the other is a 95% CI. Which one is the 95% CI and why?

Questions & Answers

QUESTION:

A random sample has been taken from a normal distribution and the following confidence intervals constructed using the same data: (37.53, 49.87) and (35.59, 51.81)

(a) What is the value of the sample mean?

(b) One of these intervals is a 99% CI and the other is a 95% CI. Which one is the 95% CI and why?

ANSWER:

Step 1 of 4

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,

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