The Basic Practice of Statistics 7th Edition

Published by W. H. Freeman
ISBN 10: 146414253X
ISBN 13: 978-1-46414-253-6

Chapter 27 - One-Way Analysis of Variance: Comparing Several Means - Chapter 27 Exercises - Page 671: 27.32

Answer

See below.

Work Step by Step

If we want to use ANOVA, then the ratio of the maximum and minimum standard deviation can be at most $2$. Here it is: $\frac{8.316}{7.409}\approx1.1224\lt2$, so we can use it. The null hypothesis says that all population means are equal to each other: $H_0:\mu_1=\mu_2=\mu_3=\mu_4$ The alternative hypothesis says the opposite of the null hypothesis, which is that at least one of the means doesn't equal all the others. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis and that the test is statistically significant. $P\lt 0.05$, thus we reject the null hypothesis. Thus there is sufficient evidence to support the claim that the sample means in the four groups differ. Group 1 has the highest average.
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