Question: a. Show that another expression for the chi-squared statistic is 2 k i1 n N pi 2 i 0 n Why

a. Show that another expression for the chi-squared statistic is 2  

k i1

n N

pi 2

i 0

  n Why is it more efficient to compute 2 using this formula?

b. When the null hypothesis is H0: p1  p2 

 pk  1/k

(i.e., pi0  1/k for all i), how does the formula of part (a)

simplify? Use the simplified expression to calculate 2 for the pigeon/direction data in Exercise 4.

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