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 } = 3.3, \sigma _ { 2 } = 1.5 \\)
sample statistics: \\( x _ { 1 } = 16, n _ { 1 } = 28, x _ { 2 } = 18, n _ { 2 } = 30 \\)

determine the alternative hypothesis.
\\( h _ { a } : \mu _ { 1 } \square \mu _ { 2 } \\)

Explanation:

Step1: Understand the null and alternative hypotheses relationship

The null hypothesis \(H_0\) is the claim to be tested. Here, the claim is \(\mu_1=\mu_2\), so \(H_0:\mu_1 = \mu_2\).
The alternative hypothesis \(H_a\) is the complement of the null hypothesis for a two - tailed test (since we are just testing if they are not equal).

Answer:

\(H_a:\mu_1
eq\mu_2\)