At the fifth hockey game of the season at a certain arena, 200 people were selected at random and asked how many of the previous four games they had attended. The results are given in Table 10.7. Test the hypothesis that these 200 observed values can be regarded as a random sample from a binomial distribution; that is, there exists a number θ (0 < θ < 1) such that the probabilities are as follows:
p0 = (1− θ)4, p1 = 4θ(1− θ)3, p2 = 6θ2(1− θ)2,
p3 = 4θ3(1− θ), p4 = θ4.
Table 10.7 Data for Exercise 2
Number of games Number of
previously attended people
0………………………………….. 33
1………………………………….. 67
2………………………………….. 66
3………………………………….. 15
4………………………………….. 19