Question

test the claim about the difference between two population means $\mu_1$ and $\mu_2$ at the level of significance $\alpha$. assume the samples are random and independent, and the populations are normally distributed.

claim: $\mu_1 = \mu_2$; $\alpha = 0.01$
population parameters: $\sigma_1 = 3.5$, $\sigma_2 = 1.7$
sample statistics: $\bar{x}_1 = 15$, $n_1 = 29$, $\bar{x}_2 = 17$, $n_2 = 30$

determine the alternative hypothesis.
$h_a: \mu_1 \square \mu_2$

Explanation:

Step1: Recall Hypothesis Testing Basics

In hypothesis testing, the alternative hypothesis \( H_a \) is the complement of the null hypothesis \( H_0 \). The claim here is \( \mu_1 = \mu_2 \), which is the null hypothesis \( H_0: \mu_1 = \mu_2 \). The alternative hypothesis for a two - tailed test (since we are testing if the means are equal and the alternative is that they are not equal when the claim is equality) is \( H_a: \mu_1
eq\mu_2 \).

Step2: Determine the Symbol

Since the null hypothesis is \( H_0: \mu_1=\mu_2 \), the alternative hypothesis (which is a two - tailed test in this case as we are testing the difference between two means and the claim is of equality) will have the symbol \(
eq \).

Answer:

\( H_a:\mu_1
eq\mu_2 \) (the symbol in the box should be \(
eq \))