The following data resprsent the frequency distribution of 200variables drawn from a parent Gaussian population with mean μ =26.00 and standard deviation Ï = 500.
The bins are two units wide and the lower edge of the first binis at x = 14.
4 8 11 20 26 31 29 22 26 13 5 2 3
(a) Plot a historgram of data.
(b) From the mean μ and standard deviation Ï, calculate theGaussian function that reprsents the parent distribution,normalized to the area of the histogram. Your first point should becalculated at x = 15, the midpoint of of the bin.
(c) Calculate Chi Squared X^2 to test the agreement between thedata and the theoretical curve.
(d) What is the expectation value of Chi Squared X^2.
(e) Refer to table C.4 to find Chi Squared X^2 probability ofthe fit, that is the probability of drawing a random sample fromthe parent population that will yield a value of Chi Squared as alarge as or larger than your calculated values.
The following data resprsent the frequency distribution of 200variables drawn from a parent Gaussian population with mean μ =26.00 and standard deviation Ï = 500.
The bins are two units wide and the lower edge of the first binis at x = 14.
4 8 11 20 26 31 29 22 26 13 5 2 3
(a) Plot a historgram of data.
(b) From the mean μ and standard deviation Ï, calculate theGaussian function that reprsents the parent distribution,normalized to the area of the histogram. Your first point should becalculated at x = 15, the midpoint of of the bin.
(c) Calculate Chi Squared X^2 to test the agreement between thedata and the theoretical curve.
(d) What is the expectation value of Chi Squared X^2.
(e) Refer to table C.4 to find Chi Squared X^2 probability ofthe fit, that is the probability of drawing a random sample fromthe parent population that will yield a value of Chi Squared as alarge as or larger than your calculated values.
