MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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A displacement sensor with digital display was used to measuring the displacement of a body impacted by a mass. Relevant sensor data is provided below. Twenty
displacement measurements are made, which yield the following:
Average measured value
20.00 [mm]
Standard deviation of measured values
0.37 [mm]
Resolution of sensor display
0.1 [mm]
Sensor Accuracy
0.5 [%] of reading
A.) If an additional measurement were to be made, calculate the range expected to contain the next measurement with 95% confidence. (i.e. the Precision Interval)
B.) Determine the uncertainty for the measured displacement at 95% probability based on all available information.
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Transcribed Image Text:A displacement sensor with digital display was used to measuring the displacement of a body impacted by a mass. Relevant sensor data is provided below. Twenty displacement measurements are made, which yield the following: Average measured value 20.00 [mm] Standard deviation of measured values 0.37 [mm] Resolution of sensor display 0.1 [mm] Sensor Accuracy 0.5 [%] of reading A.) If an additional measurement were to be made, calculate the range expected to contain the next measurement with 95% confidence. (i.e. the Precision Interval) B.) Determine the uncertainty for the measured displacement at 95% probability based on all available information.
Expert Solution
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Step 1

A).

Assume,

  • μ  be the population mean measurement.
  • be the random variable representing the measurements.
  • x be the sample mean measurement.
  • s be sample standard deviation associated with measurements.
  • n be the sample size.
  • tα2 be the value of t-statistics which corresponds to proportion of area, α2 under the right tail of t-curve with degrees of freedom n-1.

The data mentioned in the question can be written as, n=20, x=20 and s=0.37

20 measurements are being made, the range for the next measurement with 95% confidence can be given as x±tα2s1+1n.

  

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