Question

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 a 05 two-tailed and include a summary statement. b) What percentage of variance in grades is predicted from time spent wnting the exam? utes) Grade IND WE 와이고

just need b answered

Answer 1

Here Y denotes the grade the student recloves & & denotes the time (in minuates) each student spont working Let ŷ donates the expected value of y after Y is regressed upon & Then Y = a+by where a=ý -bx & b= con (EY) Vor(x) Those values are obtained from Normal equations. hance Var (7) = 6² Var (x) = con" (x, y) x Var (x) Vor (x) Van (ŷ ) = Cov?(8,4) vor (ŷ Vor (1) - con²(x,y) Zp3 Var(t) vorl) ran

n=10 Here - 8281 3458 We where psy is the square of Pearson correlation coefficient between x. and Y. Hence ply can be interpreted at the proportion of total variance in 4 that is explained by the regression equation of yonx. Hence, we calculate the correlation coefficient between X & Y from the data using formula y = con(x,y) – h Ediyi naj Var(x) Vor(7) A {a} – 3²) (+ [4; ² - 9²) Yi oci? y Xiyi 75 2916 5625 4050 Vor(x) = 57.49 4200 Vor(4) = 63.64 4136 5 = 49.9 5776 4560 g = 84.6 7921 cau(x,y) = 2.54 3249 8464 5249 p. -42.54 52 81 2704 6561 4212 Pxy √57.49663.64 2025 .49 90 2401 8100 4910 =-0.7033 499 896 254 75 722o8 9 1790 .4946 Hence. The percentage in of variation in grades that is predicted from time spent writing the exam is 49.46% or ~ 50%. كم لي 1499 3600 1936 ل ی 3600 3560 1600 92 ه لو م م 7749 3960 45 X4 ة r3