Question 384379: I know this does not have to do with algebra but I have no where else to turn! Just a simple statistics question. If you know the chi square test statistic, the degrees of freedom, and the critical value how do you calculate the p- value without a calculator looking at the chi square distribution table? Assuming the standard deviation is .1, n=10, and the test statistic is 18.585. I know you have to look at the table and subtract n-1 to get degrees if freedom but I have no idea how to calculate an exact p- value without a calculator!!!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! What kind of test is this? Are you conducting a one-tailed or a two-tailed test? If one-tailed, then are you conducting a one-tailed test to the right?
Let's just assume that we're doing a one-tailed test to the right.
First, let's bring up a chi-square table
Note: your table may look slightly different
Now because n = 10, this means that the degrees of freedom is  . So highlight the column 9 (in yellow)
Every value in this column is a chi square statistic. So because our statistic is 18.585, this means that we need to find this value in this column. However, there are only 21 numbers in this column. So we'll just try to get as close as possible. So looking through the yellow column, we find that the fourth to the last number (which is 18.48, shown in green below) gets us as close as possible to 18.585. The statistic 18.48 produces the p-value 0.03 (also shown in green below).
Notice that if we move to the next value in the column (19.68), we get the p-value 0.02. Since 18.585 is in between 18.48 and 19.68, this means that the p-value must be between 0.02 and 0.03. Since 18.585 is much closer to 18.48 than it is to 19.68, this means that the p-value associated to 18.585 is much closer to 0.03 than it is to 0.02
Note: It turns out that the p-value is 0.02897, which is very close to 0.03
So if we only had the table to rely on, the answer we would find is that the p-value is 0.03
This is of course assuming that we're doing a one-tailed test to the right.
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