At 13% significance level, there isn't enough evidence to prove the administrators to claim that the mean score for the state's eighth graders on this exam is more than 280.

<h3>How to state hypothesis conclusion?</h3>

We are given;

Sample size; n = 78

population standard deviation σ = 37

Sample Mean; x' = 280

Population mean; μ = 287

The school administrator declares that mean score is more (bigger than) 280. Thus, the hypotheses is stated as;

Null hypothesis; H₀: μ > 280

Alternative hypothesis; Hₐ: μ < 280

This is a one tail test with significance level of α = 0.13

From online tables, the critical value at α = 0.13 is z(c) = -1.13

b) Formula for the test statistic is;

z = (x- μ)/(σ/√n)

z = ((280 - 287) *√78 )/37

z = -1.67

c) From online p-value from z-score calculator, we have;

P[ z > 280 ] = 0.048

d) The value for z = -1.67 is smaller than the critical value mentioned in problem statement z(c) = - 1.13 , the z(s) is in the rejection zone. Therefore we reject H₀

e) We conclude that at 13% significance level, there isn't enough evidence to prove the administrators to claim that the mean score for the state's eighth graders on this exam is more than 280.

Read more about Hypothesis Conclusion at; brainly.com/question/15980493

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