Question 2C references: V= (4/3)pi(25.0±1.5 m)^3 Want to check my answers for th
ID: 3298305 • Letter: Q
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Question 2C references: V= (4/3)pi(25.0±1.5 m)^3
Want to check my answers for this quantitative analysis hw, I assumed that the multiplication format would be incorrect as its calculated three individual uncertainties, rather than one that simply encompasses three replicates of the same measurement. Not sure about b but assume it has to do with the tail ends of a calibration curve, thanks.
3. The "square root of the sum of the squares" uncertainty propagation equations work for uncorrelated, random errors. When the uncertainties to be combined are independent of each other, the random errors will on average tend to partially offset each other, and the combined uncertainty will be less than the simple sum of uncertainties. a. (1 pt) In question 2c, you estimated the uncertainty in the volume of a spherical droplet from the uncertainty in its radius. Explain why you would not get the correct answer if you used the rule for propagation of uncertainty in multiplication: v--(25.0±1.5 m)(25.0±1.5 m)( 25.0 ± 1.5 m) b. (1 pt) For least-squares linear regression, explain why the best-fit slope and uncertainty in an unknown concentration from a calibration curve, we have to use a more complicated equation that corrects for the "covariance" between these parameters.)Explanation / Answer
Answer:
a. This is because When the quantities contained error multiplied, the error cannot be simply added up from the propagetion rules. This is because whern multiplication done it is the relative error which gets propagated, not absolute error.
b.This is because estimates of slope intercepts (terms of b0 and b1) are not independent .These are independent when regression is centered on its sample mean. If the regression is not centered then the covarience will not be zero.
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