The table below shows the scores of 10 students for Questions A and B in the examination. Question A: 3,5,6,4,6,1,7,7,8,3 Question B: 3,5,6,4,5,8,6,5,5,3 Choose the condition of correlation coeficient R between scores of questions A and B among (a)-(e) (a) r

Question

The table below shows the scores of 10 students for Questions A and B in the examination.

Question A: 3,5,6,4,6,1,7,7,8,3
Question B: 3,5,6,4,5,8,6,5,5,3

Choose the condition of correlation coeficient R between scores of questions A and B among (a)-(e)

(a) r < -0.6 
(b) -0.6 <= r < -0.2
(c) -0.2 <= r < 0.2
(d) 0.2 <= r < 0.6
(e) r >= 0.6

styxer · Answer

$$Please\ consider\ <= as \le \ and >= as \ge $$

mathmale · Answer

Please re-arrange both sets of data in ascending order.  Then, graph them on a set of coordinate axes.  Place all the scores from Question A on the horiz. axis and all those from B on the vertical axes.  Draw an approx. regression line thru each set of points.

Estimate (visually) the slope of this regression line.

mathmale · Answer

All you need to find out from doing this is whether this slope is positive, negative, approx. zero, or ... ?  That will enable you to select the correct range of values for r.

styxer · Answer

I did it and I found something that's almost 1. However, the correct answer is not even close. I also used a correlation coefficient calculator that gave me value of R being: 0.9102.

mathmale · Answer

What about     (e) r >= 0.6    ?

mathmale · Answer

On second thought, my suggestion that you rearrange the data in ascending order is probably off-base.  Try plotting the data as is, with Set A on the horiz. axis and Set B on the vert. axis.  Again, draw a regression line through the plotted points.  Estimate r.

styxer · Answer

@mathmale Oh, now I see it. Because of the (1,8) point, it almost impossible to stabilish a relationship between the points. So, the answer (c) -0.2 <= r < 0.2 (which is the correct one) makes sense. Thank you!