4.7 Exercises on Chapter 4

**1.** Show that if the prior probability

of a hypothesis is close to unity, then the posterior probability

p0 satisfies

and more exactly

.

**2.** Watkins (1986, Section 13.3) reports that theory predicted the existence of a Z particle of mass

GeV, while first experimental results showed its mass to be

GeV. Find the prior and posterior odds and the Bayes ratio for the hypothesis that its mass is less than 93.0 GeV.

**3.** An experimental station wishes to test whether a growth hormone will increase the yield of wheat above the average value of 100 units per plot produced under currently standard conditions. Twelve plots treated with the hormone give the yields:

Find the P-value for the hypothesis under consideration.

**4.** In a genetic experiment, theory predicts that if two genes are on different chromosomes, then the probability of a certain event will be 3/16. In an ...