Page 455 - Probability and Statistical Inference

432 8. Tests of Hypotheses

unknown parameter. With preassigned α ∈ (0, 1), derive the randomized MP
level α test for H : p = p versus H : p = p where p < p are two numbers
1
1
0
0
0
1
from (0, 1). Explicitly find k and γ numerically when n = 10, 15, 25, α = .05,
.10 and p = .1, .5, .7.
0
8.3.7 (Example 8.3.7 Continued) Suppose that X , ..., X are iid random
1
n
+
variables having the Poisson(λ) distribution where λ ∈ ℜ is the unknown
parameter. With preassigned α ∈ (0, 1), derive the randomized MP level α test
for H : λ = λ versus H : λ = λ where λ < λ are two positive numbers.
0
1
0
0
1
1
Explicitly find k and γ numerically when n = 10, 15, 25, α = .05, .10 and λ =
0
1, 2.
8.3.8 Suppose that X is an observable random variable with its pdf given
by f(x), x ∈ ℜ. Consider the two functions defined as follows:
Determine the MP level α test for
in the simplest implementable form. Perform the power calculations. {Hint:
Follow the Example 8.3.8.}
8.3.9 Suppose that X , X , X are observable iid random variables with the
2
3
1
common pdf given by f(x), x ∈ ℜ. Consider the two functions defined as
follows:

Determine the MP level α test for

in the simplest implementable form. Perform the power calculations. {Hint:
Follow the Example 8.3.9.}
8.3.10 Suppose that X is an observable random variable with its pdf given
by f(x), x ∈ ℜ. Consider the two functions defined as follows:

Show that the MP level a test for