## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 7 - Estimates and Sample Sizes - 7-3 Estimating a Population Mean - Basic Skills and Concepts - Page 359: 24

#### Answer

The confidence intervals overlap, so we cannot say that the lengths of skull breadths have changed over the time.

#### Work Step by Step

We know that $α=0.05$, hence we know that $t_{α/2}=2.201$. Also, using a standard deviation calculator, we can find that the standard deviation of the 150 AD data set is $5.02$. Hence the error is: $\frac{2.201\cdot5.02}{\sqrt n}=\frac{2.201\cdot5.02}{\sqrt{12}}=3.1896$ We do the same thing for the 4000 BC data set. We know that $α=0.05$, hence we know that $t_{α/2}=2.201$. Also, using a standard deviation calculator, we can find that the standard deviation of the 4000 BC data set is $4.64$. Hence the error is: $\frac{2.201\cdot4.64}{\sqrt n}=\frac{2.201\cdot5.02}{\sqrt{12}}=3.1896$ Then, using the means as the center of the data set and the errors to determine the minimums and maximums, we can see that the data overlap, meaning that we cannot say that the lengths of skull breadths have changed over the time.

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