How Would You Think To Predict A High Grade

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Suppose that you are a fourth grade teacher and you’ve saved extensive records of all your students for the past five years. Assume that your students are a sample of all fourth graders in your state and you can use your student data to test some ideas.
1. What is the major problem with your assumption? The major problem with this assumption is that all the data collected came from the students of one particular teacher and does not represent all fourth graders in the state since these students all had two major things in common, the school and the teacher. If the teacher was an extraordinary teacher or a terrible teacher or if the school was in a really wealthy district or a really poor district than the results would be skewed. A random sample of all fourth graders would have to come from all over the state in different schools districts and different elementary schools.

2. You’re wondering if the distribution of grades was roughly Normal. How would you check this? I would do a histogram and look at the shape of the data. If the data follows a bell-shaped distribution, the Gaussian distribution, it would be considered normal.

3. You have a nagging idea that shorter students tend to have better grades; how could you check to see if there is a link between height and grades? Maybe you could roughly predict a new student’s final grade by their height? How would you do that, and how accurate might that prediction be? I would complete a scatter plot graph to look at the correlation of the data. I could make predictions based on the height by simply looking up the height and go with the corresponding grade on the line. To test how accurate my prediction would be I would then calculate the strength of the correlation (r) the closer to -1 or 1 the stronger the relationship is and the more likely my prediction would be accurate.

4. 4th graders in the US take a standardized test for math. The national average score is 237. Did your state, as represented by your students, outperform the national average using a statistically significant measure? I would figure out the average score of my students and compare them to the average score of the national students. I would then do a two sample t test for significance with the Ho = 237 and Ha > 237. If I find for Ha than my students would have outperformed the national average.

5. December holidays always seem such a distraction to 4th graders. Are your students’ December grades significantly worse than their October grades? If so, by how much? I would compare the October data with the December data and then do a paired t-test. Ho would equal the mean of the October data and Ha would be less than the mean of the October data. If I find for Ho
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