Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 13–6 The Spearman Rank Correlation Coefficient and the Runs Test 701SolutionStep 1 State the hypotheses.H 0 : r 0 and H 1 : r 0Step 2 Find the critical value. Use Table L to find the value for n 8 and a 0.05.It is 0.738. See Figure 13–3.Figure 13–3Finding the CriticalValue in Table L forExample 13–7n = 0.10 = 0.05 = 0.0256780.7389...Step 3Find the test value.a. Rank each data set as shown in the table.Bank Branches Rank Deposits RankA 209 4 23 4B 353 2 31 1C 19 8 7 6D 201 5 12 5E 344 3 26 2F 132 6 5 7G 401 1 24 3H 126 7 4 8b. Let X 1 be the rank of the branches and X 2 be the rank of the deposits.c. Subtract the ranking (X 1 X 2 ).4 4 0 2 1 1 8 6 2 etc.d. Square the differences.0 2 0 1 2 1 2 2 4 etc.e. Find the sum of the squares0 1 4 0 1 1 4 1 12The results can be summarized in a table as shown.X 1 X 2 d X 1 X 2 d 24 4 0 02 1 1 18 6 2 45 5 0 03 2 1 16 7 1 11 3 2 47 8 1 1d 2 1213–31