You buy a bag of 40 lollipops. This bag has 4 different colors of lollipops in it. You are curious if all 4 colors were equally likely to be put in the bag or whether certain colors were more likely.
If all four colors were equally likely to be put in the bag, how many lollipops of each color would you expect there to be?
If all four colors were equally likely to be put in the bag, then you would expect 1/4 of the lollipops to be each color. So, the expected frequency would be (1/4)(40) = 10. (Of course, this is the theoretical expected frequency, not what we actually expect the bag to look like.)
10
0.0
Suppose now that you open the lollipops to find out that you have 8 red, 5 green, 12 orange, and 15 blue. Test the null hypothesis that the colors of the lollipops occur with equal frequency. What is the Chi Square value you get?
Take the sum of each (expected - observed)^2/expected = (10-8)^2/10 + (10-5)^2/10 + (10-12)^2/10 + (10-15)^2/10 = 5.8
5.8
0.0
Suppose you are trying to determine whether a spinner with 8 numbers is fair or if it tends to land on certain numbers more than others. You spin this wheel 200 times. Conduct a Chi Square test based on the data below. What is your p value?
questions/chi_table.gif
The expected frequency of each number is 25. Calculate the sum of each (expected - observed)^2/expected = 3.24 + 1.96 + 1.44 + 2.56 + 6.76 + .04 + 2.56 + .64 = 19.2. Use the Chi Square Distribution Calculator to determine that the probability of getting a Chi Square value (df = 7) of 19.2 or larger if all 8 of these outcomes were equally likely is .0076.
.0076
0.00041