### Solution Found!

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

**Chapter , Problem 8**

(choose chapter or problem)

**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?

### Questions & Answers

**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?

**ANSWER:**

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