A sample of students was taken measuring the hours studied for a test and the sc
ID: 3251715 • Letter: A
Question
A sample of students was taken measuring the hours studied for a test and the score on the test (out of a possible total of 350 points)
X(# hours study) Y (Score on test)
5 155
7 210
8 150
10 192
11 245
13 260
15 270
18 275
20 290
g) What % of the variation in test scores is explained by the # hours of study?
h) What % is due to other factors?
i) Name 1 other factor that could affect a test score.
j) What is the calculated F in testing the null hyothesis: no significant relation between # hours of study and test scores. (You must use the Tool-Pak for this.)
k) What is the p-value?
l) Is there a significant relation between #hours of study and test scores? Please answer yes or no.
Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: Y (Score on test)
Independent Variable: X (# hours study)
Y (Score on test) = 116.99512 + 9.2901302 X (# hours study)
Sample size: 9
R (correlation coefficient) = 0.89329303
R-sq = 0.79797244
Estimate of error standard deviation: 25.289681
Parameter estimates:
Analysis of variance table for regression model:
g) % of the variation in test scores is explained by the # hours of study = R2 = 79.80%
h) % due to other factors = 100% - 79.80% = 20.20%
i) 1 Other factor that can affect the test score is attendance in class.
j) Calculated F = 27.65
k) p - Value = 0.0012
l) Since p - value is less than 0.05, reject Ho. Hence,
Yes, There is significant relationship between # hours of study and test scores.
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 116.99512 22.633574 0 7 5.1690962 0.0013 Slope 9.2901302 1.7667868 0 7 5.2582068 0.0012Related Questions
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