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# Spearman's rank correlation , joint probability distribution

16-26. Far West University offers both day and evening classes in business administration. One question in a survey of students inquires how they perceive the prestige associated with certain careers. Each student was asked to rank the careers from 1 to 8, with 1 having the most prestige and 8 the least prestige. The results were:

Career Ranking by Day Students Ranking by Evening Students Career Ranking by Day Students Ranking by
Evening Students
Accountant 6 3Statistician 1 7
Computer programmer7 2Marketing researcher 4 8
Branch bank manager 2 6 Stock analyst 3 5
Hospital administrator 5 4 Production manager 8 1

Find Spearman's coefficient of rank correlation.
15.5
A six-sided die is rolled 30 times and the numbers 1 through 6 appear as shown in the following frequency distribution. At the .10 significance level, can we conclude that the die is fair?
Outcome Frequency Outcome Frequency
1 3 4 3
2 6 5 9
3 2 6 7