SUPPLEMENTAL STUDY GUIDE FOR FINAL EXAM
HYPOTHESIS TESTING - REVIEW
1. Suppose that a certain university claims that at least 80% of its graduates get jobs within three months of graduation. Test this hypothesis at the .01 significance level, if a random sample of 9 students shows that only 4 got jobs within three months of graduation. Even though 4 is clearly less than 80% of 9, your result should show that you do not reject H0, (that is, you do not have enough data to say you are 99% certain that the claim is false).
2. Rework problem 1 at the .05 significance level. In what way does the result change?
3. Rework problem 1 (at the .05 significance level) if a sample of 40 students shows that only 27 got jobs within three months of graduation. How would you have to reword the problem to make this a 2-tail test? How would it change the results if you did this problem as a 2-tail test?
CONTINGENCY TABLES
4. Perform a Chi-square (c2) test to determine (at the .05 significance level) whether there is a significant relationship between success in a Physics course and a proposed prerequisite; the following table breaks down the number of Physics students in a test group according to whether or not they had the proposed prerequisite, and whether or not they succeeded in Physics:
|
|
Successful in Physics |
Not successful in Physics |
Totals |
|
Student had prerequisite |
54 |
11 |
65 |
|
Student didn’t have prerequisite |
8 |
21 |
29 |
|
Totals |
62 |
32 |
94 |
CORRELATION AND REGRESSION
Formulas (not in this form in Triola textbook)
Sxx
= 
Note: Sxx = 
which is used in the formula for standard dev.
Syy
= 
Note: Syy = 
Sxy
= 
Note: Sxy = 
Least squares regression line (line of best fit): y = b0 + b1x
Slope:
Intercept:
Since the line
of best fit passes through the point 
5. For the following collection of ordered pairs
(related x’s and y’s), calculate n, Sxx
, Syy , Sxy , 
and 
Remember that you will need to add columns for x2, y2, and xy
|
|
x |
y |
|
|
1 |
8 |
|
|
2 |
7 |
|
|
4 |
7 |
|
|
7 |
5 |
|
|
8 |
4 |
|
|
8 |
4 |
|
|
10 |
2 |
6. Calculations with a collection of ordered pairs (related x’s and y’s) result in the following values:
n=8, Sxx = 49.9, Syy =
0.34, and Sxy = -3.95,
= 17.4 and = 4.85 Use these values to:
a. Find an equation of the regression line.
b. Predict y if x is 22
c. Find the correlation coefficient.
d. Test the correlation coefficient to determine whether the relationship between x and y is significant (test at the .05 significance level)
Return to: Merced College; Don Power Updated 12/03/08 by Don Power