Question

A random sample of 75 eighth grade students' scores on a national mathematics assessment test has a mean score of 279. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 275. Assume that the population standard deviation is 34. At c = 0.03, is there enough evidence to support the administrator's claim? Complete parts (a) through (). (a) Write the claim mathematically and identify Ho and H, Choose the correct answer below. O A. Horus 275 (claim) Hu>275 O B. He: 12 275 (claim) H:<275 O E. Horus 275 H>275 (daim) OC. He: <275 H: 12 275 (claim) OF H = 275 Hu> 275 (daim) OD. Hyu-275 (claim) Hu> 275 (b) Find the standardized test statistic z, and its corresponding area. z=(Round to two decimal places as needed.) (c) Find the P-value. P-value = (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. O Reject Ho O Fail to reject Ho (e) Interpret your decision in the context of the original claim. At the 3% significance level, there enough evidence to the administrator's claim that the mean score for the state's eighth graders on the exam is more than 275.

Answer 1

Solution :

The null and alternative hypothesis are

H₀ : $\mu$ = 275    ........... Null hypothesis

H_a: $\mu$ > 275 ........... Alternative hypothesis

Here, n = 75, $\bar x$ = 279, $\sigma$ = 34

The test statistic t is

z = ($\bar x$ - $\mu$ )/[$\sigma$/$\sqrt{}$n]

= [279 - 275]/[34 /$\sqrt{}$75]

= 1.02

The value of the test​ statistic z = 1.02

Now ,

> sign in Ha indicates that the test is ONE TAILED.

z = 1.02

So , using calculator ,

p-value = P(z > 1.75)

= 0.154

p value = 0.154

Since,

p value is greater than the significance level 0.03

Decision:

Fail to Reject the null hypothesis H0

Interpret :

At the 3% significance level, there is not enough evidence to support the administrator claim thet the mean score for the state eight graders on the is more than 275.