Question

use technology and a t - test to test the claim about the population mean \\( \mu \\) at the given level of significance \\( \alpha \\) using the given sample statistics. assume the population is normally distributed.
claim: \\( \mu>71 ; \alpha = 0.01 \\) sample statistics: \\( \overline { x } = 71.3, s = 3.3, n = 25 \\)
what are the null and alternative hypotheses? choose the correct answer below.
\\( \bigcirc \\) a. \\( h _ { 0 } : \mu \geq 71 \\)
\\( h _ { a } : \mu<71 \\)
\\( \bigcirc \\) b. \\( h _ { 0 } : \mu \
eq 71 \\)
\\( h _ { a } : \mu = 71 \\)
\\( \bigcirc \\) c. \\( h _ { 0 } : \mu \leq 71 \\)
\\( h _ { a } : \mu>71 \\)
\\( \bigcirc \\) d. \\( h _ { 0 } : \mu = 71 \\)
\\( h _ { a } : \mu \
eq 71 \\)

Explanation:

The null hypothesis \(H_0\) is a statement of no - effect or equality. The alternative hypothesis \(H_A\) is the claim we are trying to find evidence for. Here, the claim is \(\mu>71\). The null hypothesis for a one - tailed (right - tailed in this case) t - test about the population mean (when the claim is \(\mu > k\)) is \(H_0:\mu\leq k\) and the alternative hypothesis is \(H_A:\mu > k\), where \(k = 71\) in this problem.

Answer:

C. \(H_0:\mu\leq71\), \(H_A:\mu > 71\)