Chapter 15.10, Problem 59E

Refer to Exercise 11.4. Regard both book and audited values as random variables and test for positive correlation between the two by using Spearman’s rank correlation coefficient. Give bounds for the p-value associated with the test.

11.4 Auditors are often required to compare the audited (or current) value of an inventory item with the book (or listed) value. If a company is keeping its inventory and books up to date, there should be a strong linear relationship between the audited and book values. A company sampled ten inventory items and obtained the audited and book values given in the accompanying table. Fit the model Y = β₀ + β₁x + ε to these data.

a What is your estimate for the expected change in audited value for a one-unit change in book value?

b If the book value is x = 100, what would you use to estimate the audited value?