Question

. A professor is interested in knowing the correlation, if any, of students’ scores on the first and second exams given in his class.



Test 1 Test 2
92 86
90 87
89 85
82 90
88 79
92 90
100 92
91 84

Is there a significant correlation? Explain its statistical significance, if any.




With respect to the situation in the above question , what other test could the professor use that would yield valid results by looking for differences. What would be the statistical result of the test?

Answer 1

Sample size, n: 8
Degrees of freedom: 6

Correlation Results:
Correlation coefficient, r: 0.3201344
Critical r: ±0.706734
P-value (two-tailed): 0.4395

Fail to Reject the Null Hypothesis
Sample does not provide enough evidence to support a linear correlation

Regression Results:
Y= b0 + b1x:
Y Intercept, b0: 62.71449
Slope, b1: 0.2642045

Total Variation: 119.875
Explained Variation: 12.28551
Unexplained Variation: 107.5895
Standard Error: 4.23457
Coefficient of Det, R^2: 0.102486

Conclusion: There is no significant correlation