In: Statistics and Probability
As a student you have probably noticed a curious phenomenon. In every class, there are some students who zip through exams and turn their papers in while everyone else is still working. Other students continue working until the very last minute. Have you ever wondered what grades these students get? Are the students who finish first the best in the class or are they simply conceding failure? To answer this question, we carefully observed a recent exam and recorded the amount of time each student spent working (X) and the grade they received (Y). The data from the sample of n = 10 students is below.
a) compute the Pearson correlation to measure the degree of relationship between the time spent writing the exam and the grade. Is the correlation statistically significant? State the null hypothesis, use α = .05 two-tailed and include a summary statement.
b) What percentage of variance in grades is predicted from time spent writing the exam?
Student | Time(in minutes)-X | Exam Grade-Y |
1 |
54 | 75 |
2 | 38 | 91 |
3 | 60 | 70 |
4 | 44 | 94 |
5 | 60 | 76 |
6 | 40 | 89 |
7 | 57 | 92 |
8 | 52 | 81 |
9 | 45 | 88 |
10 | 49 | 90 |
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