Step 1 :Given the taste ranks as [2, 9, 4, 6, 8, 3, 7, 1, 5] and price ranks as [1, 9, 7, 3, 6, 2, 5, 8, 4], we can calculate the differences between the ranks for each brand.
Step 2 :The differences are calculated as [1, 0, -3, 3, 2, 1, 2, -7, 1].
Step 3 :We then use the Spearman's rank correlation coefficient formula, which is \(r_s = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)}\), where \(d_i\) is the difference in ranks for each item and \(n\) is the number of items.
Step 4 :Substituting the values into the formula, we get \(r_s = 1 - \frac{6 \sum (1, 0, -3, 3, 2, 1, 2, -7, 1)^2}{9(9^2 - 1)}\).
Step 5 :Solving the equation, we find that the Spearman's rank correlation coefficient is approximately 0.35.
Step 6 :Thus, the value of the (Spearman's) rank correlation coefficient test statistic is \(\boxed{0.35}\).