Question

The answer to this question asap please

Answer 1

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.

How to state hypothesis conclusion?

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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