Question

What is the relationship between the amount of time statistics students study per week and their final exam scores? The results of the survey are shown below. Time Score 3 67 13 95 6 15 77 89 13 100 3 66 7 63 11 79 1 59 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? D = 0 H: ? *0 The p-value is: (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the regression line is useful There is statistically significant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying. There is statistically insignificant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying. There is statistically insignificant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the use of the regression line is not appropriate. d. pe (Round to two decimal places) e. Interpretrº There is a 79% chance that the regression line will be a good predictor for the final exam score based on the time spent studying 79% of all students will receive the average score on the final exam. There is a large variation in the final exam scores that students receive, but if you only look at students who spend a fixed amount of time studying per week, this variation on average is reduced by 79% Given any group that spends a fixed amount of time studying per week, 79% of all of those students will receive the predicted score on the final exam.

Answer 1

score (x-mean(x)) (y-mean(y)) (x-mean(x))? (y-mean(y))? (x-mean(x))*(y-mean(y)) 51.1 Islo - ০ ০ ৬ ০ ৬L -10.22 17.78 -০.22 11.78 22.78 -11.22 -14.22 1.78 -18.22 104.4484 316.1284 0.0484 138.7684 518.9284 125.8884 202.2084 3.1684 331.9684 212|| | 1741.5556|| 88.9 | 0.44 82.46 113.9 56.1 14.22 25 5.34 127.54 total 540

from the above table, EX= 72,ya 695 {(x-7) 2= 212 EN-GJ2= 1741,56 n=9, {(x-7) (4-7)=540 Mow, mean (X) = x= Et cy 185 8] and mean (y) = T = = = 695 TT = 77.221 n car Mow, .. coucx,y) = H, ECX-8)(4-7) = 540 CON (XU = 67.5

. and sample variance -) ? 1. i 212 2 Sy? E 2615 and hence Sx = 5.15 for y S7 = L sly-ij ² h- = 1741,56 8 so = 217070 henec Sy = 14.75 (a) now, sample correlation coefficient CON (XY) Ya sy sy 67.5 5.15 X 14.75 [r= 0.8g] r = 0.89

(6) Mell and alternative hypothesis Hoo P=0 Hiifto where, f is population correlation coefficient Mowe, test statistic is ter Jn-2 Noten-2) putting the values t= 0.89 x 19-2 J 1-10.89,2 tz 2:35 0.46 It= sell Now, for two tailed t-test with t= soll and in-2) = 7 dif p-value is I p-value = 0.0014 !

see that (9 for Q=0.05 we p-value La So, we reject the null hypothesis and conclude that " There is statistically signe ficant . evidenee to conclude that there is a correlation between the time spent studying and the score on the fined exam Thus, regression line is useful. therefore, first option is correct. (d) coefficient of determination, ra r2 = (oregle r2 = 0.79.21 or, (r2 = 79.21%

(e) Interpretation of 72 - 79.21% "There is a 79% chanee that the regression line will be a good predictor for the final exam score based on the time spent studying." therefore, option first is correcto