A random sample of 86 eighth grade students' scores on a national mathematics assessment test has a mean score of 291


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
40

At α =0.13 is there enough evidence to support the administrator's claim?

Complete parts (a) through (e).


Question
Part 1

(a) Write the claim mathematically and identify
Upper H0
and
Upper Ha.

Choose the correct answer below.


A.
H0: μ=285
Ha: μ >285 (claim)

B.
H0: μ=285 (claim)
Ha: μ>285


C.
H0: μ ≤285
Ha: μ>285 (claim)


D.
H0: μ<285
Ha: μ ≥285 (claim)


E.
H0: μ≥285 (claim)
Ha: μ <285



F.
H0: μ ≤285 (claim)
Ha: μ >285


Part 2
(b) Find the standardized test statistic z.

Z= ….. ?
(Round to two decimal places as needed.)


Part 3
(c) Find the P-value.

P-value = ….. ?
(Round to three decimal places as needed.)


Part 4
(d) Decide whether to reject or fail to reject the null hypothesis.

Reject H0

OR

Fail to reject H0


Part 5
(e) Interpret your decision in the context of the original claim.

At the 13% significance level, there (is OR is not) enough evidence to (support OR
reject) the administrator's claim that the mean score for the state's eighth graders on the exam is more than 285.