Q1. Calculate SP (the sum of products of deviations) for the following scores. Note: Both means are decimal values, so the computational formula works well.
X Y
10 6
4 2
8 6
0 2
8 4
Q2. Assuming a two-tailed test with α = .05, how large a correlation is needed to be statistically significant for each of the following samples?
a. A sample of n = 10
b. A sample of n = 20
c. A sample of n = 30
d. A sample of n = 40
Q3. As a student, you probably have noticed a curious phenomenon. In every class, there are some students who zip through exams and turn in their papers while everyone else is still on page 1. Other students cling to their exams and continue working until the very last minute. Have you ever wondered what grades these students get? Are the students who finish first the best in the class or are they simply conceding failure? To answer this question, we carefully observed a recent exam and recorded the amount of time each student spent working and the grade each student received. Following are data for a sample of n = 10 students.
a. Calculate the Pearson correlation between time and grade.
b. Based on the correlation, describe the relationship between time and grade. Do the highest grades go to the students who finish first or last?
Time (in minutes) Exam Grade
54 75
38 91
60 70
44 94
60 76
40 89
57 92
52 81
45 88
49 90
Q4. A set of n = 20 pairs of scores (X and Y values) has SSX = 25, SSY = 16, and SP = 12.5. If the mean for the X values is M = 6 and the mean for the Y values is M = 4,
a. Calculate the Pearson correlation for the scores.
b. Find the regression equation for predicting Y from the X values.
Q5. For the following data:
a. Find the regression equation for predicting Y from X.
b. Use the regression equation to find a predicted Y for each X.
c. Find the difference between the actual Y value and the predicted Y value for each individual, square the differences, and add the squared values to obtain SSresidual.
d. Calculate the Pearson correlation for these data. Use r2 and SSY to computeSSresidual. You should obtain the same value as in part c.
X Y
1 3
4 8
3 6
2 3
5 9
3 7
Q6. The student population at the state college consists of 55% females and 45% males.
a. The college theater department recently staged a production of a modern musical. A researcher recorded the gender of each student entering the theater and found a total of 385 females and 215 males. Is the gender distribution for theater goers significantly different from the distribution for the general college? Test at the .05 level of significance.
b. The same researcher also recorded the gender of each student watching a men's basketball game in the college gym and found a total of 83 females and 97 males. Is the gender distribution for basketball fans significantly different from the distribution for the general college? Test at the .05 level of significance.
Q7. To investigate the phenomenon of "home team advantage," a researcher recorded the outcomes from 64 college football games on one Saturday in October. Of the 64 games, 42 were won by home teams. Does this result provide enough evidence to conclude that home teams win significantly more than would be expected by chance? Assume that winning and losing are equally likely events if there is no home team advantage. Use α = .05.
Q8. A professor in the psychology department would like to determine whether there has been a significant change in grading practices over the years. It is known that the overall grade distribution for the department in 1985 had 14% As, 26% Bs, 31% Cs, 19% Ds, and 10% Fs. A sample of n = 200 psychology students from last semester produced the following grade distribution:
A B C D F
32 61 64 31 12
Do the data indicate a significant change in the grade distribution? Test at the .05 level of significance.
Q9. In a study investigating freshman weight gain, the researchers also looked at gender differences in weight (Kasparek, Corwin, Valois, Sargent, & Morris, 2008). Using self-reported heights and weights, they computed the Body Mass Index (BMI) for each student. Based on the BMI scores, the students were classified as either desirable weight or overweight. When the students were further classified by gender, the researchers found results similar to the frequencies in the following table.
Desirable Weight Overweight
Males 74 46
Females 62 18
a. Do the data indicate that the proportion of overweight men is significantly different from the proportion of overweight women? Test with α = .05.
b. Compute the phi-coefficient to measure the strength of the relationship.
Q10. Although the phenomenon is not well understood, it appears that people born during the winter months are slightly more likely to develop schizophrenia than people born at other times (Bradbury & Miller, 1985). The following hypothetical data represent a sample of 50 individuals diagnosed with schizophrenia and a sample of 100 people with no psychotic diagnosis. Each individual is also classified according to season in which he or she was born. Do the data indicate a significant relationship between schizophrenia and the season of birth? Test at the .05 level of significance.
Season of Birth
Summer Fall Winter Spring
No Disorder 26 24 22 28 n = 100
Schizophrenia 9 11 18 12 n = 50
35 35 40 40