A random sample of 81 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 266.

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A random sample of 81 eighth grade​ students'
scores on a national mathematics assessment test has a mean score
of 266. This test result prompts a state school
administrator to declare that the mean score for the​ state's
eighth graders on this assessment is more
than 260. 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 content area bottom
Part 1
​(a) Write the claim mathematically and
identify H0 and Ha. Choose the correct answer
below.
A. H0​: μ≤260
, Ha​: μ>260 ​(claim)
B. H0​: μ=260
, Ha​: μ>260 ​(claim)
C. H0​: μ=260 ​(claim) ,
Ha​: μ>260
D. H0​: μ<260
, Ha​: μ≥260 ​(claim)
E. H0​: μ≥260 ​(claim)
, Ha​: μ<260
F. H0​: μ≤260 ​(claim)
, Ha​: μ>260
Part 2
​(b) Find the standardized test statistic​ z, and its
corresponding area.
z=enter your response here
​(Round to two decimal places as​ needed.)