## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 9 - Inferences from Two Samples - 9-5 Two Variances or Standard Deviations - Basic Skills and Concepts - Page 483: 2

#### Answer

a)$s_1^2=43.56cm^2$ $s_2^2=36.2404cm^2$ b)$H_0=\sigma_1=\sigma_2$ c)$1.202.$ d) There is not sufficient evidence to support the claim that heights of men and heights of women have different variances.

#### Work Step by Step

a) We know that the sample variance is equal to the sample standard deviation squared. Hence: $s_1^2=(6.6cm)^2=43.56cm^2$ $s_2^2=(6.02cm)^2=36.2404cm^2$ b) The null hypothesis says that the population variances are equal: $H_0=\sigma_1=\sigma_2$ c) The value of the F, the test statistic is the ratio of the sample variances: $F=\frac{s_1^2}{s_2^2}=\frac{43.56}{26.2404}=1.202.$ d) If $P$ is less than the significance level, we reject the null hypothesis. $P=0.2550\gt0.10$, hence we fail to reject the null hypothesis. Hence there is not sufficient evidence to support the claim that heights of men and heights of women have different variances.

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