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. 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?

  • statistics -

    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

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