lets figure out our chi square statistic. so to figure this out, lets get our statistic, our chi square statistic. ill write it like this here for fun. or maybe ill right it as a big X because its really , this random distribution is approximately a chi square distribution. so ill write it like that. and well talk about the degrees of freedom in a second acually let me write it in a curly axis. so you see that some people write with the chi instead of the x. so our chi square statistic over here, we are literally going to find the squared distance between the observed and the expected divided by the expected which will be 20-25.3 squared over 25.3 plus 30-29.4 squared over 29.4 + 30 -25.3 squared over 25.3 and then im gonna have to do these over here so let me just continue it you can ignore this h1 over here + 100-94.7 squared over 94.7 +110-110.6 squared over 110.6 and finally 90-94.7 squared over 94.7. so we have (20-25.3) squared /25.3+(30-29.4 )squared/29.4 + (30-25.3)squared/25.3+(100-94.7)squared /94.7+(110-110.6)squared /110.6+(90-94.7)squared/94.7 we get 2.53.so our chi square statistic assuming the null hypothesis is correct is equal to 2.53 next thing we need to do is figure out the degrees of freedom we had while doing this. and ill give you the rule of thumb. that is you have the number of rows. so you have the rows and you have the number of columns so you have 2 rows and 3 columns you dont count the total. so the degrees of freedom is for your contingency table is the number of rows-1 times the number of columns-1. in our situation we have two rows and 3 columns so that will be 2-1 times 3-1. so that is going to be 2.we have 2 degrees of freedom. the reason why that should have some intuitive sense is that if you assume that you know the total. if you know all of this information, over here, if you know the total information, actually if you knew the parameters of the population as well, but if you knew the total information, and you knew this information or if you knew r-1 of the informations in the rows, the last one can be figured out if you subtract it from the otal. for example, in this situation, if you knew this, you could easily figure out this. this is not new information.l this is just total 