8.22 An activity on bias and reliability. Cut 5 pieces of string having these lengths in inches: 2.9 9.5 5.7 4.2 7.6

a. Show the pieces to another student one at a time, asking the subject to estimate the length to the nearest tenth of an inch by eye. The error your subject makes is measured value minus true value and can be either positive or negative. What is the average of the 5 errors? Explain why this average would be close to 0 if there were no bias and we used many pieces of string rather than just 5.

b. The following day, ask the subject to again estimate the length of each piece of string. (Present them in a different order on the second day.) Explain why the 5 differences between the first and second guesses would all be 0 if your subject were a perfectly reliable measurer of length. The bigger the differences, the less reliable your subject is. What is the average difference (ignoring whether they are positive or negative) for your subject?

8.24 Even more on bias and reliability. Exercise 8.22 gives five true values for lengths. A subject measures the first length (true length=2.9 inches) four times by eye. His measurements are 3.0 2.9 3.1 3.0 Suppose his measurements have a bias of +0.1 inches.

a. What are the four random errors for his measurements? b. What is the variance of his four measurements?