Chisq.test and Goodness-of-fit

I just read this article, http://ift.tt/1HArtja, specifically the section on the goodness-of-fit test. I even computed the chi-square value the old fashioned way, and got it right (13.6)!

I have a few questions:

1. From the article: "We then compare the value calculated in the formula above to a standard set of tables. The value returned from the table is 1.8%.". This is the value returned by the chisq.test in the p-value. How does the function calculate the p-value?


2. The p-value indicates that there is a 1.8% probability that the die is fair. Is this the same as saying that I am (100 - 1.8) 98.2% confident that the die is unfair?


3. Is there a way of calling the chisq.test() function passing a confidence factor of 99%?


4. Finally, should I be using the chisq.test() function on the actual observations, or on a contingency table derived from the observations?

Thank you for your help/pointers/advice.

Richard Rogers