For each of the following questions, explain your answer using full sentences. Explain how you would set up the data, state what graphs and statistics are needed, and if applicable, which Test to use and both the Ho and Ha.

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?

2. You're wondering if the distribution of grades was roughly Normal. How would you check this?

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?

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?

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?

6. You read in a magazine that at this age girls often have better grades in math than the boys. How would you determine if there is a significant difference?

7. In spite of that article, a fellow teacher feels that proportionally more of the boys pass math than the girls. Hmm, how would you test it?

8. Do more redheads fail math than students with other hair colors?