A study was conducted to compare the average time spent in the lab each week versus course grade for computer students.The results are recorded in the table below. Number of hours spent in lab Grade (percent)
10 96
11 51
16 62
9 58
7 89
15 81
16 46
10 51
Compute Spearman's rank correlation.Assume that rank ties will have little influence on your result.
A)0.017
B)-0.284
C)0.371
D)0.462
E)-0.381

Question

Quizplus · Accepted Answer

We first need to rank the hours spent in lab and the grades. After ranking, the table looks like this:
Hours (X)  Rank  Grade (Y)  Rank 
7          1     89         5 
9          2.5   58         3 
10         4     96         7 
10         4     51         2 
11         5     51         2 
15         6     81         6 
16         7.5   62         4 
16         7.5   46         1

Using the formula for Spearman's rank correlation, we get:
r = 1 - ((6*Σd^2)/(n^3-n))

where d is the difference between the two ranks, n is the number of pairs. Σd^2 is equal to 52.5.

Plugging in the values, we get:
r = 1 - ((6*52.5)/(8^3-8))
r = -0.381

Therefore, the best choice is E with an explanation that Spearman's rank correlation is -0.381.

A Study Was Conducted to Compare the Average Time Spent