## 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: 8

#### Answer

There is sufficient evidence to support that the pennies have a standard deviation more than 0.023.

#### Work Step by Step

$H_{0}:σ=0.023$. $H_{a}:σ >0.023.$ Hence the value of the test statistic: $X^2=\frac{(n−1)s^2}{σ^2}=\frac{(35-1)^2 0.0391^2}{0.023^2}=98.26.$ The critical value is the $X^2$ value corresponding to the found significance level, hence:$X_{0.05}^2=43.773.$. If the value of the test statistic is in the rejection area, then this means the rejection of the null hypothesis. Hence:43.773<98.26, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the pennies have a standard deviation more than 0.023.

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