A scientist evaluates two different digital thermometers. Each has a digital rea

Question

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.

Explanation / Answer

Part a: The largest possible error in thermometer A is infinite. If the sensor element of thermometer A was painted black, and a 1 megawatt IR laser with a very small dot diameter was shone at it, the sensor's temperature could raise by thousands of degrees within the one second it takes the display to update. Thus, for time durations of less than one second, the largest possible error is infinite.

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