Bayesian Statistics: An Introduction, 4th Edition

6.8 Exercises on Chapter 6

1. The sample correlation coefficient between length and weight of a species of frog was determined at each of a number of sites. The results were as follows: Find an interval in which you are 95% sure that the correlation coefficient lies.

2. Three groups of children were given two tests. The numbers of children and the sample correlation coefficients between the two test scores in each group were as follows: Is there any evidence that the association between the two tests differs in the three groups?

3. Suppose you have sample correlation coefficients on the basis of sample sizes . Give a 95% posterior confidence interval for .

4. From the approximation which holds for large n, deduce an expression for the log-likelihood and hence show that the maximum likelihood ...