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

Why is it more efficient 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 simplified expression to calculate x2 for the pigeon/direction data in Exercise 4.

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N? x² = i-1 прю -п