Question

3) An undergraduate psychology student has been told that the hours she spends readying for the verbal part of the GRE (a standardized test) will likely help predict how she will do on the exam. Her advisor tells her that the more hours she spends studying, the higher her grade will probably be. To test this, her advisor has comprised information from 10 psyc students in the past who have also taken the GRE and submitted the amount of study hours along with their score. Hopeful Grad Student Hours of Study GRE Score 9 240 2 45 300 3 35 280 4 270 5 25 265 6 25 260 7 90 337 8 65 330 9 20 270 10 60 300 16 a. What is the independent variable? Ib. What is the dependent variable? c. What test did you use to analyze the data? d. Is the test significant? How do you know? e. Write the statistical notation in APA style Asch. f. Report the findings in 1-3 sentences. Make sure to include the independent variable, the dependent variable, all relevant statistics and a summary,

Answer 1

The necessary calculation for test,

35 16 Hopeful Grad !Hours of study GRE score (y) s1=(x-xbar)^2 s2=ty-ybar)^2 s3=(x-xbar)*ty- 1 9 240 900 2043.04 1356 2 45 300 36 219.04 88.8 3 280 27.04 20.8 4 16 270 529 231.04 349.6 5 25 265 196 408.04 282.8 6 25 260 196 635.04 352.8 7 90 337 2601 2683.24 2641.8 8 65 330 676 2007.04 1164.8 9 20 270 361 231.04 288.8 10 60 300 441 219.04 310.8 sum 390 2852 5952 8703.6 6857 mean 39 285.2 r=sum(3)sqr 0.9526935533

where x: Hours of study , y:GRE score,

r= correlation coefficient = sum(s3)/sqrt(sum(s1)*sum(s3)) =0.9527

and xbar=mean(x) , ybar=mean(y)

a) The independent variable is: Hour of study (x)

b) The dependent variable is : GRE score (y)

c) We want test,

Is there exist any positive linear relationship between hours of study and GRE score.

so we use t-test.

d) Test statistics,

t = (r* sqrt(n-2))/sqrt(1-r^2) = (0.9527*sqrt(8))/sqrt(1-0.9527^2) = 8.8659

P-value= P(t>8.8659) = 1.035e-05

Here p=pvalue< alpha=0.05, therefore we may conclude that the result is significant.

e) t(8)=8.8659 , p=1.035e-05

f)There was a significant positive linear relationship between hours of study and GRE score. correlation coefficient (r) =0.9527, t(8)=8.8659, p=1.035e-05