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?

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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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