1.(1 pt) Using the six variables listed below, choose two variables for each of
ID: 3153493 • Letter: 1
Question
1.(1 pt) Using the six variables listed below, choose two variables for each of the following correlation coefficients: (a) r=0.01, (b) r= -0.79, (c) r=0.35, (d) r=0.91. You can use variables more than once, and there are multiple correct answers.
VARIABLES: height, weight, GPA, pant size, weekly hours of exercise, parent’s education level
2.(1 pt) For each of these sets of variables identify the independent and dependent variable, OR state that the decision is arbitrary:
a.A basketball coach looks at hours of practice and free throw shooting percentage among his players.
b.A doctor gathers data on the birth weights and adolescent weights of 20 of his long-term patients.
c.A researcher determines the number of days of sunshine and the physical activity of individuals in Denver, Colorado.
d.A physical therapist examines the relationship between upper body strength and lower body strength in a group of patients.
3.(2.5 pts) The correlation coefficient between reaction time and 40 meter sprint time is r=0.57 in a sample of 20 national-level sprinters. Test the significance of the correlation coefficient at =0.05 using the traditional hypothesis testing method.
4.(0.5 pt) When the correlation coefficient (r) is not significant, what can be said about the regression line?
(5 pts) Below is a small sample of scores on pull-ups and push-ups completed without stopping in a group of six subjects. You can use Excel to help you answer these questions.
Subject
# Pull-ups
# Push-ups
1
0
8
2
1
14
3
5
16
4
6
12
5
8
24
6
10
35
For this data:
(a) draw a scatter plot for the variables – label and scale your axes appropriately for full credit
(b) compute the value of the correlation coefficient (r)
(c) state the hypotheses
(d) test the significance of the correlation coefficient (use PPMC table for ease)
(e) give a brief explanation of the type of relationship (e.g., direction, strength)
(f) determine the slope and intercept of the regression line
(g) predict the number of push-ups for an individual who can perform 22 pull-ups
(h) determine what percent of the variation in # of push-ups can be explained by variation in # of pull-ups (i.e., the coefficient of determination)
(i) calculate the standard error of the estimate
Subject
# Pull-ups
# Push-ups
1
0
8
2
1
14
3
5
16
4
6
12
5
8
24
6
10
35
Explanation / Answer
1 a) weakly exrcise and parent's educational level. b) weight and weakly hour sof exercise c) height and weight d) GPA nd parent's educational level.
2) a) Independent-hour sof practice Dependent-free throw spercentage
b) independent-birth weights dependent-adolescent weights
c) Independent: number of days of sunshine dependent:physical activity
d) arbitrary
3) t=r/sqrt [(1-r^2)/n-2]
=0.57/sqrt [(1-0.57^2)/20-2]
=2.94
The p value is 0.004377. The p value is less than alpha=0.05, reject H0 to conclude that reaction time and 40 metre sprint time is linearly correlated.
4. The variables are linearly uncorrelated.
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