In: Statistics and Probability
Student # Days Missed in 6th Grade # Days Missed in 10th Grade
A 4 10
B 2 4
C 21 11
D 1 3
E 3 1
F 5 5
G 4 9
H 8 5
a)
The association between the number of days missed in sixth grade and the number of days missed in tenth grade is determined by Pearson correlation coefficient.
The Pearson correlation coefficient is obtained using the formula,
Where the data values are,
# Days Missed in 6th Grade, X | # Days Missed in 10th Grade, Y | ||||
4 | 10 | 16 | 100 | 40 | |
2 | 4 | 4 | 16 | 8 | |
21 | 11 | 441 | 121 | 231 | |
1 | 3 | 1 | 9 | 3 | |
3 | 1 | 9 | 1 | 3 | |
5 | 5 | 25 | 25 | 25 | |
4 | 9 | 16 | 81 | 36 | |
8 | 5 | 64 | 25 | 40 | |
Sum | 48 | 48 | 576 | 378 | 386 |
Now,
The Pearson correlation coefficient value, r = 0.6087 which indicates there is a positive correlation between two variable and the correlation value of r between 0.6 to 0.8 mean there is a strong correlation between two variable.
b)
Now, the hypothesis test for significance of the correlation coefficient is performed in following steps,
Step 1: The null and alternative hypotheses are,
Step 2: The significance level,
The critical value for the t-statistic for degree of freedom = n-2=8-2=6
(In excel use formula, =T.INV.2T(0.05,6) )
Step 3: The t-statistic is obtained using the formula,
Step 4:
Since the t-statistic is less than t-critical value, the null hypothesis is not rejected. Hence there is no significant correlation is between number of days missed in sixth grade and the number of days missed in tenth grade.