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7.3 Australian crab data: The files bluecrab.dat and orangecrab.dat contain measurements of body depth (Y1) and rear width (Y2), in millimeters, made on 50 male crabs from each of two species, blue and orange. We will model these data using a bivariate normal distribution. a) For each of the two species, obtain posterior distributions of the population mean ? and covariance matrix S as follows: Using the semiconjugate prior distributions for ? and S, set µ0 equal to the sample mean of the data, ?0 and S0 equal to the sample covariance matrix and ?0 = 4. Obtain 10,000 posterior samples of ? and S. Note that this "prior" distribution loosely centers the parameters around empirical estimates based on the observed data (and is very similar to the unit information prior described in the previous exercise). It cannot be considered as our true prior distribution, as it was derived from the observed data. However, it can be roughly considered as the prior distribution of someone with weak but unbiased information. b) Plot values of ? = (?1, ?2) 0 for each group and compare. Describe any size differences between the two groups. c) From each covariance matrix obtained from the Gibbs sampler, obtain the corresponding correlation coefficient. From these values, plot posterior densities of the correlations ?blue and ?orange for the two groups. Evaluate differences between the two species by comparing these posterior distributions. In particular, obtain an approximation to Pr(?blue < ?orange|yblue, yorange). What do the results suggest about differences between the two populations?
The sample mean of the weights of the adult women of town A is larger than the sample mean of the weights of the adult women of town B. Moreover, the sample mean of the weights of the adult men of town A is larger than the sample mean of the weigh..
Two baseball teams, the Toronto Jaybirds and the Philadelphia Cheesesteaks, are members of a fictitious baseball league. Whenever two teams in this league face each other, they play a series of up to five games. The first team to win three games w..
Linear correlation (presented in Session 5) and linear regression are closely related statistical concepts
a diagnostic test for a certain disease is applied to n individuals known to not have the disease. let x the number
pick a collection of values in reference to various variables from a web site. describe and list a few examples of your
Suppose a sample of 40 Jones & Ryan employees showed a sample mean year-end bonus of $118,000. Assume a population standard deviation of o=$30,000 and compute the p-value.
Estimating the Size of a Sample to Study
in each of the following situations the sampling frame does not match the population resulting in undercoverage. give
Compute the average of the areas. How does this compare with your guess? How does it compare with the averages of the judgment samples for the others in your group?
In order to conduct testing of the life hours of their light bulbs, they randomly sampled nine light bulbs and measured how many hours they lasted (mean = 346.6). 378, 361, 350, 375, 200, 391, 375, 368, 321 What is the variance?
Calculate all measures of central tendency for data that are interval or ratio in measurement. Calculate the standard deviation for data that are interval or ratio in measurement
For each case below, choose the most appropriate statistical procedure: A teacher of a low-level reading group is interested in what the average score is for the group of 25 students.
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