8. Spectacled weavers are birds that use grass to weave nests that look like hanging baskets. The male bird weaves a nest and then invites the female to inspect the nest. If no female accepts the nest, the male will build another nest; the male continues to build new nests until a female accepts. 200 male birds were observed, and X, the number of nests that were rejected by the females before a nest was accepted, was recorded for each male bird. The results are given in the first two columns of Table 1. The table can be found in the image: (a) Write down a possible distribution for these data, giving reasons for your choice. (b) Calculate the sample mean and standard deviation for these data and use these answers to estimate the parameter(s) for the distribution. (c) Write down the formula to calculate P(X = 2) = p2 = 0.0879 (4 dp). Show clearly how to use the answer to (b) to calculate the value given here. (d) Use the pi-values given in the table {which were obtained as in part (c), other than p4 = 1 − P(X ≤ 3)} to calculate the corresponding expected values (ei). Then do a goodness-of-fit test on these data, using a 5% level of significance.
8. Spectacled weavers are birds that use grass to weave nests that look like hanging baskets. The male bird weaves a nest and then invites the female to inspect the nest. If no female accepts the nest, the male will build another nest; the male continues to build new nests until a female accepts. 200 male birds were observed, and X, the number of nests that were rejected by the females before a nest was accepted, was recorded for each male bird. The results are given in the first two columns of Table 1. The table can be found in the image:
(a) Write down a possible distribution for these data, giving reasons for your choice.
(b) Calculate the sample mean and standard deviation for these data and use these answers to estimate the parameter(s) for the distribution.
(c) Write down the formula to calculate P(X = 2) = p2 = 0.0879 (4 dp). Show clearly how to use the answer to (b) to calculate the value given here.
(d) Use the pi-values given in the table {which were obtained as in part (c), other than p4 = 1 − P(X ≤ 3)} to calculate the corresponding
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
