A physics instructor investigates the relationship between the time, $t\,$ hours, spent by 8 students on an independent research project and their final ranking, $r$ , in a national competition. The data are recorded in the table below, with rank 1 representing the highest level of achievement.

Student	Research Time ( $t$ )	Time Rank ( $x$ )	Competition Rank ( $r$ )
A	12	7	6
B	45	2	3
C	30		5
D	18		7
E	55	1	1
F	8		8
G	22		4
H	38	3	2

Complete the ranks for the research time (assigning rank 1 to the longest time) and calculate the Spearman's rank correlation coefficient for this data.

Stating your hypotheses clearly, test at the 5% level of significance whether there is a positive correlation between the time spent on research and the competition performance. (The critical value for $n = 8$ at the 5% significance level is 0.6429).

Student	Research Time ( $t$ )	Time Rank ( $x$ )	Competition Rank ( $r$ )
A	12	7	6
B	45	2	3
C	30		5
D	18		7
E	55	1	1
F	8		8
G	22		4
H	38	3	2

Complete the ranks for the research time (assigning rank 1 to the longest time) and calculate the Spearman's rank correlation coefficient for this data.

2.2.2 Scatter diagrams and correlation

Question 109

Markscheme

2.2.2 Scatter diagrams and correlation

Question 109

Markscheme

2.2.2 Scatter diagrams and correlation

Question 109

2.2.2 Scatter diagrams and correlation Questions

2.2.2 Scatter diagrams and correlation

Question 109

2.2.2 Scatter diagrams and correlation Questions