Elementary Statistics: Picturing the World (6th Edition)

Published by Pearson
ISBN 10: 0-32191-121-0
ISBN 13: 978-0-32191-121-6

Chapter 6 - Confidence Intervals - Section 6.1 Confidence Intervals for the Mean - Exercises - Page 305: 22

Answer

31.2 < $\mu$ < 31.6

Work Step by Step

c =0.95, $\bar{x}$ = 31.39, $\sigma$ = 0.8, n = 82 Formula for CI: $\bar{x}$ $\pm$ ( z$\times$$\frac{\sigma}{\sqrt n}$) 1) The z score that corresponds to a 95% confidence level is 1.96 2) Find the margin of error 1.96 x $\frac{0.8}{\sqrt 82}$ $\approx$ 0.173 3) Find the bounds of the interval 31.39 - 0.173 = 31.217 31.39 + 0.173 = 31.563 Therefore the Confidence interval is 31.217 < $\mu$ < 31.563 $\approx$ 31.2 < $\mu$ < 31.6
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