Question

a random sample of 78 eighth grade students scores on a national mathematics assessment test has a mean score of 277. this test result prompts a state school administrator to declare that the mean score for the states eighth graders on this exam is more than 270. assume that the population standard deviation is 36. at \\( \alpha = 0.08 \\), is there enough evidence to support the administrators claim? complete parts (a) through (e).
(a) write the claim mathematically and identify \\( h _ { 0 } \\) and \\( h _ { a } \\). choose the correct answer below.
\\( \bigcirc \\) a. \\( h _ { 0 } : \mu \leq 270 \\) (claim)
\\( h _ { a } : \mu > 270 \\)
\\( \bigcirc \\) b. \\( h _ { 0 } : \mu \geq 270 \\) (claim)
\\( h _ { a } : \mu < 270 \\)
\\( \bigcirc \\) c. \\( h _ { 0 } : \mu \leq 270 \\)
\\( h _ { a } : \mu > 270 \\) (claim)
\\( \bigcirc \\) d. \\( h _ { 0 } : \mu = 270 \\)
\\( h _ { a } : \mu > 270 \\) (claim)
\\( \bigcirc \\) e. \\( h _ { 0 } : \mu = 270 \\) (claim)
\\( h _ { a } : \mu > 270 \\)
\\( \bigcirc \\) f. \\( h _ { 0 } : \mu < 270 \\)
\\( h _ { a } : \mu \geq 270 \\) (claim)

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) is a statement of equality or no difference. The alternative hypothesis \(H_a\) is the claim we are trying to find evidence for. The administrator's claim is that the mean score \(\mu> 270\). The null hypothesis is the opposite of the claim (for one - tailed tests of this type). So \(H_0:\mu\leq270\) and \(H_a:\mu > 270\) (where the claim is \(H_a\)).

Answer:

C. \(H_0:\mu\leq270\), \(H_a:\mu > 270\) (claim)