10. a. Show that another expression for the chi-squared statistic is Why is it more ef cient...

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10.

a. Show that another expression for the chi-squared statistic is Why is it more ef cient to compute x2 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 simpli ed expression to calculatex2 for the pigeon/direction data in Exercise 4.

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