PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Data analysis and model fitting in the laboratory · Data analysis and model fitting in the laboratory
Mathematical Methods for Physics, Ch Estimation, fitting and hypothesis testing
Problem
Three different straight-line fits, each to N=22 points with the intercept and the gradient both fitted, give minimised values χ2=18.5, χ2=45.0 and χ2=3.0.
((a)) State the number of degrees of freedom ν, and the expected value and standard deviation of the minimised χ2.
((b)) For each fit, find how many standard deviations its χ2 lies from the expected value.
((c)) Say what each result signals about the model or the quoted errors.