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Describe a real-world problem using a single sample t-test

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The principal of your local school announces to the school-community group (of which you are a part) that funding will be cut next year if a higher percentage of the children in the 4th, 5th, and 6th grades do not perform at the expected level of proficiency on the state test. Your principal knows you are a graduate student and assumes you are an expert in statistics and research design. She would like you to help the school find out if the children are performing at or below the state norm on these tests.

Bring to mind a real-world situation or problem that could be addressed using a single-sample t test. For this situation or problem:

1. Give a brief description of the real-world situation or problem
2. Clearly identify the independent and dependent variables you would study.
3. Generate the statistical null and alternative hypotheses.
4. Describe what information the effect size would tell you that the probability value would not.
5. Using realistic numbers for values of degrees of freedom, sample size, and t statistic, report hypothetical results in a few sentences using correct APA format.