A random sample of 88 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 288. This test result prompts a state school administrator to declare that the mean score for the​ state's eighth graders on this exam

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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11. 

A random sample of
88
eighth grade​ students' scores on a national mathematics assessment test has a mean score of
288.
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
280.
Assume that the population standard deviation is
36.
At
α=0.09​,
is there enough evidence to support the​ administrator's claim? Complete parts​ (a) through​ (e).
 
 
 
​(a) Write the claim mathematically and identify
H0
and
Ha.
Choose the correct answer below.
 
 
A.
H0​:
μ≤280
Ha​:
μ>280
​(claim)
Your answer is correct.
 
B.
H0​:
μ=280
Ha​:
μ>280
​(claim)
 
C.
H0​:
μ=280
​(claim)
Ha​:
μ>280
 
D.
H0​:
μ<280
Ha​:
μ≥280
​(claim)
 
E.
H0​:
μ≥280
​(claim)
Ha​:
μ<280
 
F.
H0​:
μ≤280
​(claim)
Ha​:
μ>280
​(b) Find the standardized test statistic​ z, and its corresponding area.
 
z=enter your response here
​(Round to two decimal places as​ needed.)
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