Data set 4.3.30 is of a study to see if there is a relationship between number o
ID: 3207375 • Letter: D
Question
Data set 4.3.30 is of a study to see if there is a relationship between number of hours a student studies each week and the student’s age. Is there sufficient evidence to conclude that a linear relationship exists?
A Correlation coefficient = 0.2995; no, there does not appear to be a significant relationship.
B Correlation coefficient = 0.547; yes, there appears to be a positive linear relationship.
C Correlation coefficient = 0.547; no, there does not appear to be a significant relationship.
D Correlation coefficient = 0.2995; yes, there appears to be a weak linear relationship.
Age, x Hours Studying. y 18 4.2 18 1.1 18 4.6 18 3.1 18 5.3 18 3.2 19 2.8 19 2.3 19 3.2 19 5.1 19 2.3 20 1.7 20 6.1 20 3.2 20 5.3 21 2.5 21 6.4 21 4.2 22 2.1 22 3.6 24 5.4 25 4.8 25 3.9 26 5.2 26 4.2 35 8.1Explanation / Answer
Enter the data in Excel-Data-Data Analysis-Correlation-enter A1:B26 in Input range-enter F4 in Output range-click Ok.
The Pearson correlation coefficient, r=0.5473.
The relationship is positive and moderate linear relationship between age and hours of studying.
Compute t test statistic and corresponding p value to find if the relationship is significant or not.
H0:p=0 (age and hours of studying are linearly uncorrelated)
H1:p>0 (age and hours of studying arepositively linearly correlated)
t=r/sqrt{(1-r^2)/(n-2)}, where, n denotes number of pairs(x,y).
=0.5473/sqrt(1-0.5473^2)/(26-2)}
=3.20
p value at 24 degrees of freedom (df=n-2) is: 0.004.
The p value is less than 0.05, therefore, reject H0, and conclude that there appears to be a positive linear relationship.
Option B.
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