A scientist evaluates two different digital thermometers. Each has a digital read-out to the nearest one degree, and updates once each second. When the temperature is held constant, the digital display of thermometer A does not change, but the display of thermometer B randomly toggles between three to four adjacent readings (i.e., +/- 2 degrees). For the questions below, assume that the temperature is held constant.
a. What is the largest possible error in an individual reading from A?
b. What is the largest possible error in an individual reading from B?
c. In a single reading, which provides the "best" information? Explain.
d. If 1000 readings are taken with A, what is the standard deviation?
e. If 1000 readings are taken with B, what is the approximate standard deviation? (choose from 0.1, 0.5, 2.0 and 4.0).
f. If 1000 readings are taken with thermometer B, what is the "typical error between the mean of the readings, and the mean of the underlying process?
g. If 1000 readings are taken with each thermometer, which data set provides the "best" information? Explain.
h. How many readings must be taken with thermometer A to reliably detect a temperature change of 0.15 degrees? (choose from 10, 100, 1000, 1 million, 1 billion, or "it cannot be done"). Explain.
i. Repeat (h) for thermometer B.