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Laboratory physics question on uncertainty

  1. May 11, 2014 #1
    1. The problem statement, all variables and given/known data

    321321.png

    2. Relevant equations

    Mean difference and SEM

    3. The attempt at a solution

    Would the mean difference be 0.16?. I'm not sure about the answer because they give that much working space, Do I have to find the uncertainty of the difference first and then my answer implement that into my answer to be 0.16 +- (uncertainty)?. How would I calculate the uncertainty of the mean difference? Do I just add the SEM's for both means?
     
    Last edited: May 11, 2014
  2. jcsd
  3. May 11, 2014 #2

    mfb

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    2016 Award

    Staff: Mentor

    Sure. The large working space is a bit odd.
    That is part (ii).
    No. Use the method (hopefully) described in section 1.5.
     
  4. May 11, 2014 #3
    Here are the basic rules for uncertainty:

    Addition/Subtraction
    $$(A ± ΔA) + (B ± ΔB) = (A+B) ± (ΔA+ΔB)$$
    $$(A ± ΔA) - (B ± ΔB) = (A-B) ± (ΔA+ΔB)$$

    When dividing and multiplying, changing to relative uncertainty, then converting back simplifies things.
    where: $$ε = \frac{ΔA}{A}*100$$ 'relative uncertainty'

    $$(A ± ΔA) / (B ± ΔB) = (A/B) ± (ε_A+ε_B)$$
    $$(A ± ΔA)(B ± ΔB) = (AB) ± (ε_A+ε_B)$$

    Then you can convert back to abs. uncertainty.
     
  5. May 11, 2014 #4

    tms

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    Are you sure? I believe the uncertainties should not simply be added, but added in quadrature. That is, if
    [tex]x = au \pm bv, [/tex]
    then
    [tex]\sigma_x^2 = a^2 \sigma_u^2 + b^2 \sigma_v^2.[/tex]
    This comes from the basic definition: If [itex]x[/itex] is a function of measured variables [itex]u, v, \ldots[/itex],
    [tex]x = f(u, v, \ldots),[/tex]
    then,
    [tex]\sigma_x^2 \approx \sigma_u^2 \left ( \frac{\partial x}{\partial u}
    \right )^2 + \sigma_v^2 \left ( \frac{\partial x}{\partial v} \right )^2 + \ldots \;.[/tex]

    I did not check your other equations.
     
  6. May 12, 2014 #5

    mfb

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    2016 Award

    Staff: Mentor

    Yes, in general the uncertainties should be added in quadrature, if correlations are not important.

    A linear addition is sometimes used as worst case estimate to include possible correlations between the uncertainties. We take the difference between measured heights here - there is no way the uncertainties could be correlated "the wrong way" (e. g. a systematic deviation towards larger men and smaller women at the same time).
     
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