91Ó°ÊÓ

2. Suppose that a random variable X has the F distribution with three and eight degrees of freedom. Determine the value of c such that Pr(X>c) = 0.975

Suppose that X₁,….., X_n forms a random sample from the normal distribution with unknown mean µ and unknown variance σ². Classify each of the following hypotheses as either simple or composite:

a) H₀ : µ = 0 and σ=1

b) H₀ : µ > 3 and σ<1

c) H₀ : µ = -2 and σ²<5

d) H₀ : µ = 0