The Woodmill Company makes windows and door trim products. The first step in the process is to rip dimension (2 × 8, 2 × 10, etc.) lumber into narrower pieces. Currently, the company uses a manual process in which an experienced operator quickly looks at a board and determines what rip widths to use. The decision is based on the knots and defects in the wood.
A company in Oregon has developed an optical scanner that can be used to determine the rip widths. The scanner is programmed to recognize defects and to determine rip widths that will optimize the value of the board. A test run of 100 boards was put through the scanner and the rip widths were identified. However, the boards were not actually ripped. A lumber grader determined the resulting values for each of the 100 boards assuming that the rips determined by the scanner had been made. Next, the same 100 boards were manually ripped using the normal process. The grader then determined the value for each board after the manual rip process was completed. The resulting data, in the file Woodmill, consist of manual rip values and scanner rip values for each of the 100 boards.
a. Develop a frequency distribution for the board values for the scanner and the manual process.
b. Compute appropriate descriptive statistics for both manual and scanner values. Use these data along with the frequency distribution developed in part a to prepare a written report that describes the results of the test. Be sure to include in your report a conclusion regarding whether the scanner outperforms the manual process.
c. Which process, scanner or manual, generated the most values that were more than 2 standard deviations from the mean?
d. Which of the two processes has the least relative variability?