10fg per question because i am broke!
QUESTION ONE
Using the data, test to see if there is a statistically significant relationship between the grade on the first test and the final average at the 0.05 level of significance. Use the formulas in this chapter and Appendix D.

Data: Students in a management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follows:

STUDENT 1 2 3 4 5 6 7 8 9

1st test grade 98 77 88 80 96 61 66 95 69

Final average 93 78 84 73 84 64 64 95 76


This post was edited by n00bMg on Oct 7 2013 10:28pm

What kind of relationship? Are they asking for correlation constant, covariance, a full-blown regression, etc?

use t-test with equal variance assumed

A t-test on what hypothesis?

From the question given, the only way I see a t-test being used is on the regression coefficient (null coeffcient ~N(0,sigma)). Otherwise, testing a hypothesis on the distribution of the test scores (whether each person's test scores are approx normally distributed about their mean) is not really relevant to the question.

This post was edited by zackill4 on Oct 8 2013 09:41am

4-13
Students in a management science class have just received
their grades on the first test. The instructor
has provided information about the first test grades
in some previous classes as well as the final average
for the same students. Some of these grades have
been sampled and are as follows:
STUDENT 1 2 3 4 5 6 7 8 9
1st test grade 98 77 88 80 96 61 66 95 69
Final average 93 78 84 73 84 64 64 95 76

(a) Develop a regression model that could be used to
predict the final average in the course based on
the first test grade.
(b) Predict the final average of a student who made
an 83 on the first test.
(c) Give the values of r and for this model. Interpret
the value of in the context of this problem.


4-14
Using the data in Problem 4-13, test to see if there is
a statistically significant relationship between the
grade on the first test and the final average at the
0.05 level of significance. Use the formulas in this
chapter and Appendix D.





i want to answer 4-14, is it required that i must also do 4-13 since it requires data from 4-13? and will that solve the mystery of what the question 4-14 is really asking? because i have no idea what they are asking... hence why i'm in need of help here

This post was edited by n00bMg on Oct 8 2013 11:27am

4-13 partially done for you here

Ok, since we're only relating the 1st test with the mean, I don't think we need to go into panel data regressions here

A simple regression model would be

mean_test_i = beta_1 * 1st_test_i + beta_0, i indexing students (the regression coefficient estimates will be the same for all students)

Once you've estimated your coefficients (there should be formulas in your book to do this, or software), then you can plug in 83 for first test to predict a mean_test score

By r, I'm taking it to mean the Pearson correlation coefficient? If so, this just indicates how correlated the two variables are and whether this is a negative or positive correlation (sign of coefficient indicates sign of correlation). More technically, its square, the R squared value, would indicate the proportion of the total variation observed in mean test scores explained by the variation in 1st test scores (usually a stats course asks for the interpretation of this).


4-14 is a piece of cake once you've calculated your beta coefficient. Just follow the formulas in your book to find the standard error of the beta_1 and test it with a null hypothesis of ~N(0, SE^2)

This post was edited by zackill4 on Oct 8 2013 02:37pm