cases, whereas one as large as 15.09 would only be expected by chance in 1% of the cases. Stated another way, it is more likely that you'll get a little deviation from the expected (thus a lower Chi-Square value) than a large deviation from the expected. The column that we need to concern ourselves with is the one under "0.05". Scientists, in general, are willing to say that if their probability of getting the observed deviation from the expected results by chance is greater than 0.05 (5%), then we can accept the null hypothesis. In other words, there is really no difference in actual ratios.......any differences we see between what Mars claims and what is actually in a bag of M&Ms just happened by chance sampling error. Five percent! That is not much, but it's good enough for a scientist. If however, the probability of getting the observed deviation from the expected results by chance is less than 0.05 (5%) then we should reject the null hypothesis. In other words, for our study, there is a significant difference in M&M color ratios between actual store-bought bags of M&Ms and what the Mars Co. claims are the actual ratios. Stated another way...any differences we see between what Mars claims and what is actually in a bag of M&Ms did not just happen by chance sampling error