4 & 5. Statistics, Quality Assurance and Calibration Methods
Confidence Intervals
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From the examples given above, find the 90% confidence interval.
A
0.009 ± 0.002758
B
0.009 ± 0.003589
C
0.009 ± 0.003961
D
0.009 ± 0.002581
Verified step by step guidance1
Identify the given data points and their associated uncertainties: 0.009 ± 0.002758, 0.009 ± 0.003589, and 0.009 ± 0.002581.
Recognize that the problem involves calculating a confidence interval, which is a range of values that is likely to contain the true value of a parameter with a specified level of confidence, in this case, 90%.
Understand that the confidence interval can be calculated using the formula: CI = mean ± (t * standard deviation / sqrt(n)), where 't' is the t-value for the desired confidence level, 'standard deviation' is the measure of data dispersion, and 'n' is the number of observations.
Calculate the mean of the given data points. Since all data points have the same mean value of 0.009, the mean remains 0.009.
Determine the combined uncertainty by considering the largest uncertainty value among the given data points, which is 0.003589, and use it to calculate the confidence interval.
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