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The temperature of a fluid in a chemical manufacturing process is measured 25 times. It can be assumed, that there is in fact no change in the temperature of the fluid at all. Nevertheless the measurement instrument determines the following values: Measurement number: 1 2 3 4 7 8 Measured value: 49.98 49.49 50.06 49.96 49.96 49.94 49.77 50.04 49.88 Measurement number: 10 11 12 13 14 15 16 17 18 Measured value: 49.83 50.11 50.02 49.78 50.01 | 49.75 50.13 50.23 50.00 Measurement number: 19 20 21 22 23 24 25 Measured value: 50.13 49.49 50.00 49.80 49.98 49.84 49.77 Table 1: Measured temperatures. a) Sketch a histogram of the measured values! b) Calculate the sample mean and the sample variance! c) Assume that the variance is constant for any temperature level. A new measurement is carried out and the measurement instrument displays a temperature of 75°C. In which range will the true temperature be, if we accept a maximum error probability of 0.3%? d) What can be done to improve the accuracy of the temperature measurement without changing the measurement, instrument?

The temperature of a fluid in a chemical manufacturing process is measured 25 times. It can be assumed, that there is in fact no change in the temperature of the fluid at all. Nevertheless the measurement instrument determines the following values: Measurement number: 1 2 3 4 7 8 Measured value: 49.98 49.49 50.06 49.96 49.96 49.94 49.77 50.04 49.88 Measurement number: 10 11 12 13 14 15 16 17 18 Measured value: 49.83 50.11 50.02 49.78 50.01 | 49.75 50.13 50.23 50.00 Measurement number: 19 20 21 22 23 24 25 Measured value: 50.13 49.49 50.00 49.80 49.98 49.84 49.77 Table 1: Measured temperatures. a) Sketch a histogram of the measured values! b) Calculate the sample mean and the sample variance! c) Assume that the variance is constant for any temperature level. A new measurement is carried out and the measurement instrument displays a temperature of 75°C. In which range will the true temperature be, if we accept a maximum error probability of 0.3%? d) What can be done to improve the accuracy of the temperature measurement without changing the measurement, instrument?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Exercise 5.6 Temperature Measurement The temperature of a fluid in a chemical manufacturing process is measured 25 times. It can be assumed, that there is in fact no change in the temperature of the fluid at all. Nevertheless the measurement instrument determines the following values: Measurement number: 1 2 3 4 5 7 8 Measured value: 49.98 49.49 50.06| 49.96 49.96 49.94 49.77 50.04 49.88 Measurement number: 10 11 12 13 14 15 16 17 18 Measured value: 49.83 50.11 50.02 49.78 50.01 49.75 50.13 50.23 50.00 Measurement number: 19 20 21 22 23 24 25 Measured value: 50.13 49.49 50.00 | 49.80 49.98 49.84 49.77 Table 1: Measured temperatures. a) Sketch a histogram of the measured values! b) Calculate the sample mean and the sample variance! c) Assume that the variance is constant for any temperature level. A new measurement is carried out and the measurement instrument displays a temperature of 75°C. In which range will the true temperature be, if we accept a maximum error probability of 0.3%? d) What can be done to improve the accuracy of the temperature measurement without changing the measurement instrument?
Transcribed Image Text:Exercise 5.6 Temperature Measurement The temperature of a fluid in a chemical manufacturing process is measured 25 times. It can be assumed, that there is in fact no change in the temperature of the fluid at all. Nevertheless the measurement instrument determines the following values: Measurement number: 1 2 3 4 5 7 8 Measured value: 49.98 49.49 50.06| 49.96 49.96 49.94 49.77 50.04 49.88 Measurement number: 10 11 12 13 14 15 16 17 18 Measured value: 49.83 50.11 50.02 49.78 50.01 49.75 50.13 50.23 50.00 Measurement number: 19 20 21 22 23 24 25 Measured value: 50.13 49.49 50.00 | 49.80 49.98 49.84 49.77 Table 1: Measured temperatures. a) Sketch a histogram of the measured values! b) Calculate the sample mean and the sample variance! c) Assume that the variance is constant for any temperature level. A new measurement is carried out and the measurement instrument displays a temperature of 75°C. In which range will the true temperature be, if we accept a maximum error probability of 0.3%? d) What can be done to improve the accuracy of the temperature measurement without changing the measurement instrument?
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