Glass fragments found on a suspect’s shoes or clothes are often used to connect the suspect to a crime scene. The index of refraction is the fragments are compared to the refractive index of the glass from the crime scene. To make this comparison rigorous, we need to know the variability the index of refraction is over a pane of glass. Bennet et al. (2002) analyzed the refractive index in a pane of float glass, searching for any spatial pattern. Here are samples of the refractive index from the edge and from the middle of the pane.

For these data, y¯1 = 1.51999, y¯2 = 1.52001, σ1 = .00002257, and σ2 = .00003075.

(a) Suppose glass at the edge of the pane is normal (µ1, σ2 1), where σ1 = .00003. Calculate the posterior distribution of µ1 when you use a normal (1.52000, .00012) prior for µ1.

(b) Suppose glass in the middle of the pane is normal (µ2, σ2 2), where σ2 = .00003. Calculate the posterior distribution of µ2 when you use a normal (1.52000, .00012) prior for µ2.

(c) Find the posterior distribution of µd = µ1 − µ2.

(d) Find a 95% credible interval for µd.

(e) Perform a Bayesian test of the hypothesis H0 : µd = 0 versus µd = 0 at the 5% level of significance.
The last half of the twentieth century saw great change in the role of women in New Zealand society. These changes included education, employment, family formation, and fertility, where women took control of these aspects of their lives. During those years phrases such as "women’s liberation movement" and "the sexual revolution"
were used to describe the changing role of women in society. In 1995 the Population Studies Centre at the University of Waikato sponsored the New Zealand Women Family, Employment, and Education Survey (NZFEE) to investigate these changes.
A random sample of New Zealand women of all ages between 20 and 59 was taken, and the women were interviewed about their educational, employment, and personal history. The details of this survey are summarized in Marsault et al. (1997). Detailed analysis of the data from this survey is in Johnstone et al. (2001).