Help with Spearman's rank correlation

Question

A university course was taught by 2 different professors.Students could choose whether to attend the lectures given by professor Q or the lecture by professor R. At the end of the course, all student took the same exams.

The test of a random sample of 30 students taught by professor Q and a random sample of 24 students taught by professor R were ranked. The sum of the ranks of the students taught by professor Q was 726 .

Test at 5% significant level whether there is difference in the ranks of the students taught by the two professors.

Answer 1

There does not appear to be adequate information to analyze this problem.

Consider a typical Spearman problem where a Personnel Manager interviews 10 job applicants for one position and ranks their abilities to hold the job. He then has the Assistant Personnel Manager interview

and rank the applicants as well.

Applicants-----------------------------Jerry---Mike---Kim---Tammy---Jake---Steve---Angela---Frank---Emily---Jo

Manager's Ranking-------------------10------9--------1--------5---------4----------2----------8----------3---------6------7

Assistant Manager's Ranking-------7-------3--------2--------8---------4--------10----------5----------1---------9------6

Difference Between Rankings------3-------6------(-1)-----(-3)--------0--------(-8)---------3----------2-------(-3)-----1

Square Of Difference-----------------9------36--------1--------9---------0--------64----------9----------4---------9------1

The Spearman Rank Correlation Coefficient is given by r_s = 1 − 6∑d²/(n³−n) or "one minus the ratio of (six times the sum of the squares of the differences) to (the sample size cubed minus the sample size). Here r_s comes to 1 − 6(142)/990 or 0.139139139... equivalent to 0.1394.

Now state the null and alternative hypotheses:

H₀: There is little or no correlation (similarity) between the rankings.

H₁: There is significant correlation (similarity) between the rankings.

Next enter a Table Of Critical Values For Spearman Rank Correlation with the arguments α=0.05 (5% significance level) and n=10 (sample size). The table will return a critical value of r_c=0.648.

In this case |0.1394|<0.648 so one fails to reject H₀. That is to say, there is little or no correlation (similarity) between the rankings.