Advanced High School Statistics: Third Edition

This distribution has three degrees of freedom, so only the row with 3 degrees of freedom (df) is relevant. This row has been italicized in the table. Next, we see that the value 6.25 falls in the column with upper tail area 0.1. That is, the shaded upper tail of Figure B.4.(a) has area 0.1. This example was unusual, in that we observed the exact value in the table. In the next examples, we encounter situations where we cannot precisely estimate the tail area and must instead provide a range of values.

The cutoff 4.3 falls between the second and third columns in the 2 degrees of freedom row. Because these columns correspond to tail areas of 0.2 and 0.1, we can be certain that the area shaded in Figure B.4.(b) is between 0.1 and 0.2.

Looking in the row with 5 df, 5.1 falls below the smallest cutoff for this row (6.06). That means we can only say that the area is greater than 0.3.

The value 11.7 falls between 9.80 and 12.02 in the 7 df row. Thus, the area is between 0.1 and 0.2.