Question

a random sample of 75 eighth grade students scores on a national mathematics assessment test has a mean score of 283. 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 280. assume that the population standard deviation is 39. at $\alpha = 0.03$, 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. $h_0: \mu \leq 280$ (claim) $\bigcirc$ b. $h_0: \mu \geq 280$ (claim) $\bigcirc$ c. $h_0: \mu < 280$
$h_a: \mu > 280$ $h_a: \mu < 280$ $h_a: \mu \geq 280$ (claim)
$\bigcirc$ d. $h_0: \mu = 280$ (claim) $\bigcirc$ e. $h_0: \mu \leq 280$ $\bigcirc$ f. $h_0: \mu = 280$
$h_a: \mu > 280$ $h_a: \mu > 280$ (claim) $h_a: \mu > 280$ (claim)

Explanation:

Step1: Understand the claim

The claim is that the mean score for the state's eighth - graders on this exam is more than 280. The null hypothesis \(H_0\) is a statement of equality or no difference, and the alternative hypothesis \(H_a\) is the claim we are trying to find evidence for.

Step2: Formulate \(H_0\) and \(H_a\)

The null hypothesis \(H_0\) is \(\mu\leq280\) (the opposite of the claim for the purpose of hypothesis testing). The alternative hypothesis \(H_a\) (the claim) is \(\mu > 280\)

Answer:

E. \(H_0:\mu\leq280\), \(H_a:\mu > 280\) (claim)