Question

A random sample of 82 eighth grade students' scores on a national mathematics assessment test has a mean score of 292. 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 285. Assume that the population standard deviation is 30. At α=0.14 is there enough evidence to support the administration's claim? Complete parts (a) through (e).

a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below.

(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

Reject H0 OR Fail to reject H0

(e) Interpret your decision in the context of the original claim.

At the 14 % significance level, there (IS/IS NOT) enough evidence to (SUPPORT/REJECT) the administrator's claim that the mean score for the state's eighth-graders on the exam is more than 285.

Answer 1

Solution :

This is the more tailed test .

The null and alternative hypothesis is ,

H₀ :   = 285

H_a : > 285

Test statistic = z

= ( - ) / / n

= (292 - 285) / 30 / 82

= 2.11

P(z > 2.11) = 1 - P(z < 2.11) = 0.0174

P-value = 0.0174

= 0.14

P-value <

Reject the null hypothesis .

At the 14 % significance level, there IS enough evidence to SUPPORT the administrator's claim that the mean score for the state's eighth-graders on the exam is more than 285.