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You're 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.
For each of the following questions, state what test to use, how you would set up the data and the Ho/Ha if applicable. Please use full sentences.
What's the major problem with your assumption?

It is highly unlikely that the students in one class are representative of all classes. Especially since schools generally mimic the social make-up of the surrounding community. If this school is in an impoverished neighborhood, wealthier neighborhoods will be underrepresented in the sample and vice versa.

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

You could look at a histogram and look for that tell-tale bell shape. More analytically, you could look at a P-P plot and see if the plot of points follows a straight line. Additionally, you could run an Anderson-Darling test for normality (or other test) to obtain a p-value for normality. A low p-value would indicate non-normality.

You have a nagging idea that shorter students tend to have better grades; maybe you could roughly predict a new student's final grade by their height? And how accurate might that prediction be?

You could run a regression to determine if there is any linear correlation between height and grades. If there is a relationship, the R^2 value will be high or the p-value for the significance of the regression coefficients will be low. If this is the case, the accuracy of the prediction depends on the amount of variability in grade that is explained by using height as a predictor variable.

4th-graders in the US take a standardized test for math. The national average score is 237. Did your state outperform the national average?

I don't know. There is no output or results provided.

December holidays always seem such a distraction to 4th graders. Are December grades significantly worse than their October grades? If so, by how much?

Again, there's no data, no output, no way to answer this question.

You read in a magazine that, at this age, girls often have better grades in math than the boys. Is it significant?

Again. No data.

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

You could do a 2-sample t-test to compare the means of the 2 groups (boys/girls)

Maybe the girls' scores vary more than the boys'?

You could do an F-test to test for equal (unequal) variance.

Redheads are rumored to have fiery tempers. Is there any significant difference in grades between blondes, brunettes, and redheads?

Don't know. There's no data.

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

No data.

If you could provide the data, I'd be glad to work on these answers.

Let me know.

Expert:	Greg
Pos. Feedback:	99.6 %
Accepts:	1165
Answered:	12/19/2008

Graduate Student

I teach math and statistics at a college level as a graduate teaching assistant