Performance in online courses. Florida State University information scientists a
ID: 3332235 • Letter: P
Question
Performance in online courses. Florida State University information scientists assessed the impact of online courses on student performance (Educational Technology & Society, Jan. 2005). Each in a sample of 24 graduate students enrolled in an online advanced Web application course was asked, “How many courses per semester (on average) do you take online?” Each student’s performance on weekly quizzes was also recorded. The information scientists found that the number of online courses and the weekly quiz grade were negatively correlated at r = -.726.
a. Give a practical interpretation of r.
b. The researchers concluded that there was a “significant negative correlation” between the number of online courses and the weekly quiz grade. Do you agree?
Agent Orange and Vietnam vets. Chemosphere (Vol. 20, 1990) published a study of Vietnam vet- erans exposed to Agent Orange (and the dioxin 2,3,7,8-TCDD). The next table (p. 154) gives the amounts of 2,3,7,8-TCDD (measured in parts per trillion) in both blood plasma and fat tissue drawn from each of the 20 veterans studied. One goal of the researchers is to determine the degree of lin- ear association between the level of dioxin found in blood plasma and fat tissue. If a linear associa- tion between the two variables can be established, the researchers want to build models to predict (1) the blood plasma level of 2,3,7,8-TCDD from the observed level of 2,3,7,8-TCDD in fat tissue and (2) the fat tissue level from the observed blood plasma level.
(a) Find the prediction equations for the researchers. Interpret the results.
(b) Test the hypothesis that fat tissue level (x) is a useful linear predictor of blood plasma level (y). Use = .05.
(c) Test the hypothesis that blood plasma level (x) is a useful linear predictor of fat tissue level (y). Use = .05.
(d) Intuitively, why must the results of the tests, parts b and c, agree?
Veteran TCDD levels in plasma TCDD levels in fat tissue
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PLEASE SHOW IN EXCEL IF POSSIBLE SO I CAN SEE HOW THE ANSWER CAN ABOUT.
1 2.5 4.92
3.1 5.9 3 2.1 4.4 4 3.5 6.9 5 3.1 7 6 1.8 4.2 7 6.8 10 8 3 5.5 9 36 41 10 4.7 4.4 11 6.9 7 12 3.3 2.9 13 4.6 4.6 14 1.6 1.4 15 7.2 7.7 16 1.8 1.1 17 20 11 18 2 2.5 19 2.5 2.3 20 4.1 2.5Explanation / Answer
a) r = - 0.726
This is the correlation between number of online courses and the weekly quiz grade.
Since r is negative, the number of online courses and weekly quiz grade are negatively (inversely) correlated. As the number of courses increases the weekly quiz grade decreases.
b)
Since r is close to -1, there is a strong negative correlation between the number of online courses and weekly quiz grade.
By significant negative correlation if the researchers mean strong negative correlation is true, if r is somewhere near -0.3 which is close to 0 then they can say it is a weak negative correlation.
The researchers are hence correct in saying that there is a significant negative correlation.
a)
prediction equation with fat as y (to be predicted) and plasma as x (explanatory variable)
fat = slope * plasma + intercept
fat = 0.9*plasma -0.15
next,
prediction equation with plasma as y (to be predicted) and fat as x (explanatory variable)
plasma = slope * fat + intercept
fat = 0.98*plasma +0.97
b)
To test if fat is a linear predictor of plasma, the predicted fat means should be equal to original fat means
For 2 tailed test, p-value is less than 0.05 and hence fat is not a linear predictor of fat.
c)
To test if plasma (x) is a good predictor of fat(y), get the predicted y for each x and compare it against the original y.
using t-test in excel (data analysis plugin)
p-value for two tail is 1 hence donot reject null hypothesis, therefore plasma is a linear predictor of fat.
TCDD plasma TCDD fat plasma-plasmaBAR fat-fatbar (plasma-plasmaBAR)^2 (fat-fatbar)^2 (plasma-plasmaBAR)*(fat-fatbar) 4.9 2.5 2 4 4 12 7 5.9 3.1 1 3 1 9 3 4.4 2.1 2 4 6 15 10 6.9 3.5 (0) 3 0 6 (0) 7 3.1 (0) 3 0 9 (0) 4.2 1.8 3 4 7 18 11 10 6.8 (3) (1) 10 1 2 5.5 3 1 3 2 9 4 41 36 (34) (30) 1,166 898 1,023 4.4 4.7 2 1 6 2 3 7 6.9 (0) (1) 0 1 0 2.9 3.3 4 3 16 7 11 4.6 4.6 2 1 5 2 3 1.4 1.6 5 4 30 20 24 7.7 7.2 (1) (1) 1 1 1 1.1 1.8 6 4 33 18 24 11 20 (4) (14) 17 195 58 2.5 2 4 4 19 16 18 2.3 2.5 5 4 21 12 16 2.5 4.1 4 2 19 4 8 6.86 6.03 1,362 1,256 1,227