## Related questions with answers

identify the claim and state $H_0$ and $H_a$.

Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal. The well-being index is a way to measure how people are faring physically, emotionally, socially, and professionally, as well as to rate the overall quality of their lives and their outlooks, for the future. The table shows the well-being index scores for a sample of states from four regions of the United States. At $\alpha=0.10$, can you reject the claim that the mean score is the same for all regions?

$\begin{matrix} \text{Northeast} & \text{Midwest} & \text{South} & \text{West}\\ \text{61.7} & \text{61.6} & \text{61.0} & \text{64.0}\\ \text{63.6} & \text{61.8} & \text{60.8} & \text{63.0}\\ \text{62.6} & \text{61.4} & \text{63.1} & \text{63.5}\\ \text{61.8} & \text{63.2} & \text{62.3} & \text{63.2}\\ \text{62.1} & \text{61.7} & \text{60.5} & \text{61.8}\\ \text{63.5} & \text{62.9} & \text{62.0} & \text{62.6}\\ \text{ } & \text{62.9} & \text{61.3} & \text{62.5}\\ \text{ } & \text{63.7} & \text{60.5} & \text{62.8}\\ \text{ } & \text{ } & \text{62.3} & \text{62.5}\\ \text{ } & \text{ } & \text{61.5} & \text{ }\\ \text{ } & \text{ } & \text{63.1} & \text{ }\\ \end{matrix}$

Solution

VerifiedThe null hypothesis states that all population means are equal:

$H_0: \mu_1=\mu_2=\mu_3=\mu_4$

The alternative hypothesis states the opposite of the null hypothesis:

$H_1:\text{ not all of } \mu_1, \mu_2, \mu_3, \mu_4\text{ are equal}$

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