Question

For the Bernoulli:

1a) Determine the most powerful critical region for testing
H_{0} p=p_{0} against H_{1} p=p_{1}
(p_{1} > p_{0}) using a random sample of size
n.

1b) Find the uniformly most powerful H_{0}
p<p_{0} against H_{1} p>p_{1}

Answer #1

**Solution:**

Let X1, X2, . . . , Xn be a random sample from the normal
distribution N(µ, 36). (a) Show that a uniformly most powerful
critical region for testing H0 : µ = 50 against H1 : µ < 50 is
given by C2 = {x : x ≤ c}. Find the values of c for α = 0.10.

Let X1, X2, . . . , X12 denote a random sample of size 12 from
Poisson distribution with mean θ.
a) Use Neyman-Pearson Lemma to show that the critical region
defined by
(12∑i=1) Xi, ≤2
is a best critical region for testing H0 :θ=1/2 against H1
:θ=1/3.
b.) If K(θ) is the power function of this test, find K(1/2) and
K(1/3). What is the significance level, the probability of the 1st
type error, the probability of the 2nd type...

Consider the test of H0: varience = 15 against H1: variance >
15. What is the critical value for the test statistic chi-square
for the significance level alpha = 0.05 and sample size n =
18

Assuming that, in testing H0:
μ
=20 vs. H1
μ
≠20, you decide on the critical region X bar ≤ 15 and
X bar ≥ 25. Assume X is normally distributed, σ
2
= 25, and the following four random values
are observed: 9, 20, 15, 11.
a) Would you accept or reject H
0
?
b) What level of
α
is assumed here?
c) What probability value would you report?
d) What would be the appropriate critical region for...

3. Suppose you are testing H0 : = 10 vs H1 : 6= 10: The sample
is small (n = 5) and the data come from a normal population. The
variance, 2, is unknown. (a) Find the critical value(s)
corresponding to = 0:10. (b) You find that t = -1.78. Based on your
critical value, what decision do you make regarding the null
hypothesis (i.e. do you Reject H0 or Do Not Reject H0)?

7. Suppose you are testing H0 : µ = 10 vs H1 : µ 6= 10. The
sample is small (n = 5) and the data come from a normal population.
The variance, σ 2 , is unknown. (a) Find the critical value(s)
corresponding to α = 0.10. (b) You find that t = −1.78. Based on
your critical value, what decision do you make regarding the null
hypothesis (i.e. do you Reject H0 or Do Not Reject H0)?

1. In order to test H0: µ=40 versus H1: µ > 40, a random
sample of size n=25 is obtained from a population that is known to
be normally distributed with sigma=6.
. The researcher decides to test this hypothesis at the α =0.1
level of significance, determine the critical value.
b. The sample mean is determined to be x-bar=42.3, compute the
test statistic z=???
c. Draw a normal curve that depicts the critical region and
declare if the null...

Suppose you want to test H0: u
<=100 against H1: u>
100 using a significance level of 0.05. The population is normally
distributed with a standard deviation of 75. A random sample size
of n = 40 will be used. If u = 130, what
is the probability of correctly rejecting a false null hypothesis?
What is the probability that the test will incorrectly fail to
reject a false null hypothesis?

Suppose that we are testing H0: μ = μ0 versus H1: μ < μ0 with
sample size of n = 25. Calculate bounds on the P -value for the
following observed values of the test statistic (use however many
decimal places presented in the look-up table. Answers are
exact):
(h) upper bound upon t0 = -1.3.
THE ANSWER IS NOT 0.15 OR 0.05

You want to test H0: µ ≤ 10.00 against H1: π > 10.00 using α
= 0.01, given that a sample of size = 25 found ?̅= 12.9 and s =
6.77.
a. What is the estimated standard error of ?̅, assuming that the
null hypothesis is correct?
b. Should your test statistic be a Z or a T (which, ZSTAT or
TSTAT)?
c. What is the attained value of the test statistic?
d. What is/are the critical values of...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 12 minutes ago

asked 14 minutes ago

asked 39 minutes ago

asked 50 minutes ago

asked 52 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago