Question

A random sample of 87 eighth grade students’ scores on a national mathematics assessment

Answer 1

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:

$\mathbf{H_o \leq 283}$

The alternative hypothesis:

$\mathbf{H_i > 283}$

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

$\mathbf{Z = \dfrac{\hat X - \mu _o}{\dfrac{\sigma}{\sqrt{n}}}}$

$\mathbf{Z = \dfrac{283 -280}{\dfrac{37}{\sqrt{87}}}}$

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:
brainly.com/question/16251072

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