## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 8 - Hypothesis Testing - 8-5 Testing a Claim About a Standard Deviation or Variance - Basic Skills and Concepts - Page 430: 13

#### Answer

There is sufficient evidence to support ages have a standard deviation less than 22.5.

#### Work Step by Step

$H_{0}:σ=22.5$. $H_{a}:σ<22.5.$ Hence the value of the test statistic: $X^2=\frac{(n−1)s^2}{σ^2}=\frac{(15-1)^2 7.67^2}{22.5^2}=1.629.$ The critical value is the $X^2$ value corresponding to the found significance level, hence:$X_{1-0.01}^2=4.66$. If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:1.629<4.66, hence wereject the null hypothesis. Hence we can say that there is sufficient evidence to support ages have a standard deviation less than 22.5.

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