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A random sample of 87 eighth grade students’ scores on a national mathematics assessment
test has a mean score of 283. The test results prompts a state school administrator to declare
that the mean score for the eighth graders on the exam is more than 280. Assume the
population deviation is 37. At α = 0.14, is there enough evidence to support the administrator’s
claim?

Respuesta :

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There is not enough evidence to support the administrator’s claim and the true mean is not significantly greater than 280.

What is a statistical hypothesis?

A hypothesis to test the given parameters requires that we determine if the mean score of the eighth graders is more than 283, thus:

The null hypothesis:

[tex]\mathbf{H_o \leq 283}[/tex]

The alternative hypothesis:

[tex]\mathbf{H_i > 283}[/tex]

From the population deviation, the Z test for the true mean can be computed as:

[tex]\mathbf{Z = \dfrac{\hat X - \mu _o}{\dfrac{\sigma}{\sqrt{n}}}}[/tex]

[tex]\mathbf{Z = \dfrac{283 -280}{\dfrac{37}{\sqrt{87}}}}[/tex]

Z = 0.756

Note that, since we are carrying out a right-tailed test, the p-value for the test statistics is expressed as follows:

P(z > 0.756)

P = 0.225

Since the P-value is greater than the significance level at α = 0.14, we can conclude that there is not enough evidence to support the administrator’s claim and the true mean is not significantly greater than 280.

Learn more about hypothesis testing here:
https://brainly.com/question/16251072

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