# In an ecological study of the feeding behavior of birds,

Chapter , Problem 8

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QUESTION:

In an ecological study of the feeding behavior of birds, the number of hops between flights was counted for several birds. For the following data,

(a) fit a geometric distribution,

(b) find an approximate 95% confidence interval for p,

(c) examine goodness of fit.

(d) If a uniform prior is used for p, what is the posterior distribution and what are the posterior mean and standard deviation?

QUESTION:

In an ecological study of the feeding behavior of birds, the number of hops between flights was counted for several birds. For the following data,

(a) fit a geometric distribution,

(b) find an approximate 95% confidence interval for p,

(c) examine goodness of fit.

(d) If a uniform prior is used for p, what is the posterior distribution and what are the posterior mean and standard deviation?

a) The geometric distribution can be used to fit this data if each hop is thought of as a trial resulting in either success or failure, where success represents the completion of a flight. The estimated probability of success can be given by p = x/n, where x = number of successes and n = number of trials.

b) To estimate a 95% confidence interval, the following equation can be used: 95% CI = [p? ± 1.96(?p?(1-p?)/n]. Using the