1) (a) A high school counselor would like to know if there is a relationship between mathematical skill and verbal skill. A sample of n = 25 students is selected, and the counselor records achievement test scores in mathematics and English for each student. The Pearson correlation for this sample is r = +0.50. Do these data provide sufficient evidence for a real relationship in the population? Test at the .05 a level, two tails.
(b) It is well known that similarity in attitudes, beliefs, and interests plays an important role in interpersonal attraction. Thus, correlations for attitudes between married couples should be strong and positive. Suppose a researcher developed a questionnaire that measures how liberal or conservative one's attitudes are. Low scores indicate that the person has liberal attitudes, while high scores indicate conservatism. Here are the data from the study:
Couple A: Husband - 14, Wife - 11
Couple B: Husband - 7, Wife - 6
Couple C: Husband - 15, Wife - 18
Couple D: Husband - 7, Wife - 4
Couple E: Husband - 3, Wife - 1
Couple F: Husband - 9, Wife - 10
Couple G: Husband - 9, Wife - 5
Couple H: Husband - 3, Wife - 3
Test the researcher's hypothesis with a set at .05.
(c) A researcher believes that a person's belief in supernatural events (e.g., ghosts, ESP, etc) is related to their education level. For a sample of n = 30 people, he gives them a questionnaire that measures their belief in supernatural events (where a high score means they believe in more of these events) and asks them how many years of schooling they've had. He finds that SSbeliefs = 10, SSschooling = 10, and SP = -8. With a = .01, test the researcher's hypothesis.
(d) To measure the relationship between anxiety and test performance, a researcher asked his students to come to the lab 15 minutes before they were to take an exam in his class. The researcher measured the students' heart rates and then matched these scores with their exam performance after they had taken the exam. Use the data below to conduct a hypothesis test for the correlation between anxiety and test performance in the population. Use a = .05.
Student Heart rate Exam score
A 76 78
B 81 68
C 60 88
D 65 80
E 80 90
F 66 68
G 82 60
H 71 95
I 66 84
J 75 75
K 80 62
L 76 51
M 77 63
N 79 71
_______________________________________________
2) Make a scatterplot and compute the regression equation for (b-d) from part 1.
3) Download the cheese.sav datafile.
a) Perform a simple bivariate linear regression analysis using Taste as the response variable and Acetic as the explanatory variable. Summarize the results carefully (hint. scatterplots of the data and the residuals may be helpful).
b) repeat (a) with taste as the response variable, and H2S as the explanatory variable.
c) repeat (a) with taste as teh response variable, and Lactic as the explanatory variable.
d) Carry out a multiple regression using Acetic and H2S to predict Taste. Summarize your results.
e) Carry out a multiple regression using H2S and Lactic to predict Taste. Summarize your results.
f) Carry out a multiple regression using H2S, Acetic, and Lactic to predict taste. Summarize your results.
g) In your opinion, which model is the "best" model to predict taste? Explain why.
4) Suppose that you are interested in whether there is a relationship between gender and educational level (undergraduate vs. graduate students) at ISU (year 2002). That is, are men and women equally likely to pursue a graduate education relative to an undergraduate education. Test whether educational level and gender at ISU are independent. Use an alpha level of 0.05.
| Student level | ||||
| Undergraduate | Graduate | |||
| Sex | Male | 7,715 | 938 | |
| Female | 10,780 | 1,625 | ||
5) Conceptual questions.
b) Know when to use which test.
c) Why are outliers (extreme values) problematic for correlational and regression analyses?
d) What is the General Linear Model? What are the "parts" of the model? (equation of line and a measure of the error around the line)
e) What are residual plots and why they are useful?