Chi Squared and Gaussian Population Question

[a1sh1teru]

The following data represent a frequency distribution of 200 variables drawn from a parent Gaussian population with mean=26.00 and standard deviation=5.00. the bins are 2 units wide and the lower edge of the first bin is at x=14.
4;8;11;20;26;31;29;22;26;13;5;2;3

a. plot a histogram of these data
b. from the mean and standard deviation, calculate the Gaussian function that represents the parent distribution, normalized to the area of the histogram. Your first point should be calculated at x=15, the midpoint of the first bin.
c. calculated (chi-squared) to test the agreement between the data and the theoretical curve.
d. what is the expectation value of (chi-squared)?
e. refer to (chi-squared) distribution table to find the (chi-squared) probability of the fit, that is, the probability of drawing a random sample from the parent population that will yield a value of (chi-squared) as large as or larger than your calculated value.


I have plotted the histogram of the data and I believe I have figured out part B... however I am having great difficulty with part C. I was given the answer already (14.2) but I can't seem to figure out how to get it from the data provided.

I'm REALLY lost with this problem, any and all help with it would be greatly appreciated.
Thank you so much.

 

[diggy]

To determine the chi-square statistic, you take the difference of your data and the theoretical curve at each bin, square it and then sum those up.

In slightly more detail:
First calculate what your theoretical Gaussian value should be at each histogram bin center.
Then take the value of each real-data histogram bin, and find the difference.
Square each difference.
Sum those squares.
Then compare that value (your measured chi-square statistic) with the expected Chi-square value in your table. Hint the table's Chi-square is based on the number of degrees of freedom you have.

There is actually a bit of theory behind all of this, but ignoring all of that for now, that is what you want to do.