Question

suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. suppose that the following data are randomly collected from five teenagers in each region of the country. the numbers represent the age at which teenagers obtained their drivers licenses.

state the alternative hypothesis.

a. ( h_{a} ) at least any two of the group means ( mu_{1}, mu_{2}, ldots, mu_{5} ) are not equal.

b. ( h_{a} ) all the group means ( mu_{1}, mu_{2}, ldots, mu_{5} ) are not equal.

c. ( h_{a} ) all the group means ( mu_{1}, mu_{2}, ldots, mu_{5} ) are equal.

d. ( h_{a} ) all the group means ( mu_{1}, mu_{2}, ldots, mu_{5} ) are higher than 0.

Explanation:

In hypothesis testing for ANOVA (Analysis of Variance), the null hypothesis \(H_0\) is that all group means are equal (\(\mu_1=\mu_2=\cdots=\mu_k\), where \(k = 5\) in this case). The alternative hypothesis \(H_a\) is the opposite of the null hypothesis. It does not require all group means to be different. It just needs at least two of the group means to be different.

Answer:

A. \(H_a\): At least any two of the group means \(\mu_1,\mu_2,\cdots,\mu_5\) are not equal.