Question

use the given statistics to complete parts (a) and (b). assume that the populations are normally distributed. (a) test whether \\( \mu _ { 1 } > \mu _ { 2 } \\) at the \\( \alpha = 0.01 \\) level of significance for the given sample data. (b) construct a \\( 99 \\% \\) confidence interval about \\( \mu _ { 1 } - \mu _ { 2 } \\). (a) identify the null and alternative hypotheses for this test. \\( \bigcirc \mathrm { a } \\). \\( h _ { 0 } : \mu _ { 1 } > \mu _ { 2 } \\) \\( h _ { 1 } : \mu _ { 1 } = \mu _ { 2 } \\) \\( \bigcirc \mathrm { b } \\). \\( h _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \\) \\( h _ { 1 } : \mu _ { 1 } > \mu _ { 2 } \\) \\( \bigcirc \mathrm { c } \\). \\( h _ { 0 } : \mu _ { 1 } \
eq \mu _ { 2 } \\) \\( h _ { 1 } : \mu _ { 1 } = \mu _ { 2 } \\) \\( \bigcirc \mathrm { d } \\). \\( h _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \\) \\( h _ { 1 } : \mu _ { 1 } < \mu _ { 2 } \\) \\( \bigcirc \mathrm { e } \\). \\( h _ { 0 } : \mu _ { 1 } < \mu _ { 2 } \\) \\( h _ { 1 } : \mu _ { 1 } = \mu _ { 2 } \\) \\( \bigcirc \mathrm { f } \\). \\( h _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \\) \\( h _ { 1 } : \mu _ { 1 } \
eq \mu _ { 2 } \\)

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) is a statement of no difference or equality. The alternative hypothesis \(H_1\) is what we are trying to find evidence for. Here, we want to test if \(\mu_1>\mu_2\). So the null hypothesis is \(H_0:\mu_1 = \mu_2\) (assuming no difference initially) and the alternative hypothesis is \(H_1:\mu_1>\mu_2\) (the claim we are testing).

Answer:

B. \(H_0:\mu_1=\mu_2\), \(H_1:\mu_1 > \mu_2\)