Question

a random sample of 75 eighth grade students scores on a national mathematics assessment test h 289. this test result prompts a state school administrator to declare that the mean score for the stat this exam is more than 280. assume that the population standard deviation is 31. at \\( \alpha = 0.15 \\), is ther to support the administrators claim? complete parts (a) through (e). \\( z = 2.51 \\) (round to two decimal places as needed.) (c) find the p - value. \\( p - value = 0.006 \\) (round to three decimal places as needed.) (d) decide whether to reject or fail to reject the null hypothesis. reject \\( h _ { 0 } \\) fail to reject \\( h _ { 0 } \\)

Explanation:

Step1: Recall the decision rule for hypothesis testing

If \(P - value\leq\alpha\), we reject the null hypothesis \(H_0\). If \(P - value>\alpha\), we fail to reject the null hypothesis \(H_0\).

Step2: Compare the P - value and \(\alpha\)

We are given that \(P - value = 0.006\) and \(\alpha=0.15\). Since \(0.006<0.15\) (i.e., \(P - value\leq\alpha\)).

Answer:

Reject \(H_0\)