Individual Homework Assignment:

This assignment has two parts:

Part I:

This data file contains two entries: year and departure temperature from the average world wide temperature in 1900 which is set to 0.0 Thus you have 107 years worth of data and each year is independent.

Your task is to use the chi-squared method to compare the data against some linear model or a combination of different linear models if you think that is better, E.g. suppose your model is that the average temperature of the earth will rise 1.0 degrees C every hundred years (or 0.1 degrees per decade).

You should compute the chi^2 statistic and try to find the linear model that produces the lowest chi^2 sum.

This is relatively easy to do within Excel for lots of different combinations once you have the data in there.

Don't be anal about this by doing the calculation on a per year basis (unless you want excel to be anal for you). You can average the data in 10 year intervals if you want. In general, averaging noisy data is a good thing to do so you might want to play around with this. When you do this, however, make sure you think about how this effects the number of degrees of freedom.

Basically you want to test the data against various linear models, e.g. 0.5 C, 1.0 C, 1.5 C, 0.3 C or whatever, per century. You should also fit a series of linear models over different time periods if you feel that a single line doesn't adequately fit the data and compared the chi^2 statistic with the previous values.

Show all your work and also, from your model, predict the tempearture in the year 2050 and assess the uncertainty in your prediction.

Part II:

The psychology department wants to determine if student gender is linked with area of interest in the field of psychology. A survey is distributed to psychology majors, who are instructed to endorse one (and only one) interest area.


          Clinical      Social        Biological 

Men           15           23            10 
Women          8           25            40

Perform a two-way chi-square analysis to test the null hypothesis that there is no relation between gender and interest area.