It is hypothesized that when homing pigeons are disoriented

It is hypothesized that when homing pigeons are disoriented in a certain manner, they will exhibit no preference for any direction of flight after takeoff (so that the direction X should be uniformly distributed on the interval from 0o to 360o). To test this, 120 pigeons are disoriented, let loose, and the direction of flight of each is recorded; the resulting data follows. Use the chi-squared test at level 0.10 to see whether the data supports the hypothesis. Direction 10-45° 45-

Solution

We expect 120/8 = 15 on each direction.

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
11   15   1.066666667  
17   15   0.266666667  
17   15   0.266666667  
15   15   0  
13   15   0.266666667  
19   15   1.066666667  
17   15   0.266666667  
11   15   1.066666667  
       0  
       0  
       0  
       0  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    4.266666667 = 4.27 [ANSWER]