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].
My sister, Lilly, and I used to have a great time playing with jelly.pdf
1. My sister, Lilly, and I used to have a great time playing with jelly beans. First we would place
them in groups on the living room floor. Then we would pretend they were rabbits and we were
hawks. We would swoop down and eat them up. Once time in particular, Lilly got the first shoot.
She ate one-fifth of the jelly bean. I went next and I ate one-sixth of the jelly beans on the floor.
Lilly then let out a shriek and ate two-fifths of the remaining beans. I then ate two-thirds of the
ones left. After Lilly ate one-half of the remainning jelly beans, there were two yellow beans left,
which we shared. How many jelly beans did each of us eat?
Solution
For this kind of problem, you have to work backwards. Since you ended up with two, right after
Lilly ate 1/2 of the beans, multiply by its reciprocal 2. 2x2=4 To get four, you ate 2/3 of what
you had before, which means 1/3 (1-2/3) were left. So multiply 4 by 3. 4x3=12 To get to those
12, Lilly had just eaten 2/5 of the remaining beans, therefore 3/5 (1-2/5) were left. 12x(5/3)= 20
To get to those 20, You ate 1/6, leaving 5/6 of the jelly beans there. 20x(6/5)=24 And finally to
get to those 24, Lilly ate 1/5, leaving 4/5. 24x(5/4)=30
This gives that you ate 4+8+1 and Lilly ate 6+8+2 +1
So, all together, you ate 13 and Lilly ate 17, starting with a total of 30 and ending with 0.
