Question 5
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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.
<h3>What is a statistical hypothesis?</h3>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:
The alternative hypothesis:
From the population deviation, the Z test for the true mean can be computed as:
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:
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