Question

i would like to ask the answer in this prob.
3.A statistics instructor at a large western university would like to examine the link (if any) between the number of optional homework problems students do during the semester and their final course grade. She randomly selects 12 students for study and asks them to keep track of the number of these problems completed during the course of the semester. At the end of the class each student’s ttal is recorded along with their final grade. Test statistic = 0.885 with α = 0.05; df = 10; tcrit = ± 2.228 and tcalc = 6.0.

Answer 1

The decision graphic

$H_0:\rho=0$

$H_1:\rho\not=0$

Reject $H_0.$

At a significance level of 0.05 we can conclude that there is a significant linear correlation between the number of homework assignments and a student’s final grade. Furthermore, we can conclude that this correlation is +

$$t_{calc}={r\over \sqrt{{1-r^2\over n-2}}}=6.0$$

$n=12$

$$36\cdot{1-r^2\over 10-2}=r^2$$ $$36-36r^2=8r^2$$

$$r^2={9\over 11}, r>0$$

$$r={3\sqrt{11}\over 11}\approx0.905$$