Question

1.Suppose we are testing a set of hypotheses using a significance level of 0.05. For which of the following p-values would we reject the null hypothesis? Select all that apply.

A. 0.06

B. 0.11

C. 0.02

D. 0.005

2. To increase the power of a hypothesis test, we can (select all that apply):

A. Increase the sample size

B. Decrease the sample size

C. Increase the significance level

D. Decrease the significance level

Answer #1

Quest 1 : We reject thehthe when we have the p value<0.05

Therefore we reject the null hypothesis at OPTION(C) 0.02 AND OPTION(D) 0.005

Quest2:

To increase the power of the test we have to INCREASE THE SAMPLE SIZE OPTION(A) and INCREASE THE LEVEL OF SIGNIFICANCE OPTION(C).

As greater the sample size greater eill be the power.

For significant level: As we decrease the significant level, the acceptance region increases ans we are less likely to reject the null hypothesis when it is false and we are more likely to commit Type 2 error.

Hence the power reduce as level of significance reduces and vice versa.

Hence ans are

Q1 - (c) and (d)

Q2 - (a) and (c)

You are testing the following hypothesis: H0: m = 72 HA: m ≠ 72
Your sample size if n = 36 and your sample standard deviation is
equal to 12. If your sample mean is equal to 69.2, the appropriate
conclusion would be to reject the null hypothesis at a significance
level of... Select one:
Select one:
a. 0.10
b. 0.05
c. 0.02
d. 0.01
e. None of the above.

Suppose that before we conduct a hypothesis test we pick a
significance level of ?. When the test is conducted, we get a
p-value of 0.023. Given this p-value, we
a. can reject the null hypothesis for any significance level, ?,
greater than 0.023.
b. cannot reject the null hypothesis for a significance level,
?, greater than 0.023.
c. can reject the null hypothesis for a significance level, ?,
less than 0.023.
d. draw no conclusion about the null hypothesis.

In hypothesis testing, what is the level of significance?
SELECT ALL CORRECT OPTIONS
OPTION A
A value between 0 and 1.
OPTION B
The risk of rejecting the null hypothesis when it is true.
OPTION C
It is selected before a decision rule can be formulated.
OPTION D
All apply.

1. The P-value of a test of the null hypothesis is
a. the probability the null hypothesis is true.
b. the probability the null hypothesis is false.
c. the probability, assuming the null hypothesis is false, that
the test statistic will take a value at least as extreme as that
actually observed.
d. the probability, assuming the null hypothesis is true, that
the test statistic will take a value at least as extreme as that
actually observed.
2. The P-value...

What is the decision at a 0.05 level of significance for each of
the following tests? Hint: Find the critical value for each test;
then make a decision. (Round your critical values to two decimal
places.) Part (a) F(3, 25) = 3.03 Fcrit = Retain the null
hypothesis. Reject the null hypothesis. Part (b) F(5, 22) = 2.47
Fcrit = Retain the null hypothesis. Reject the null hypothesis.
Part (c) F(4, 35) = 2.71 Fcrit = Retain the null hypothesis....

What is the decision at a 0.05 level of significance for each of
the following tests? Hint: Find the critical value for each test;
then make a decision. (Round your critical values to two decimal
places.) Part (a) F(3, 27) = 3.00 Fcrit = Retain or reject the null
hypothesis. Part (b) F(5, 17) = 2.61 Fcrit = retain or reject the
null hypothesis Part (c) F(4, 36) = 2.70 Fcrit = retain or reject
the null hypothesis Part (D)...

True or False:
(a) The generalized likelihood ratio statistic Λ (the one we use
when the hypotheses are composite, i.e., we must use the MLE
estimator in the denominator) is always less than or equal to
1.
(b) If the p-value is 0.03, the corresponding test will reject
at the significance level 0.02.
(c) If a test rejects at significance level 0.06, then the
p-value is less than or equal to 0.06.
(d) The p-value of a test is the...

What is the decision at a 0.05 level of significance for each of
the following tests? Hint: Find the critical value for each test;
then make a decision. (Round your critical values to two decimal
places.)
Part (a) F(3, 26) = 3.04
Fcrit =
Retain the null hypothesis.
Reject the null hypothesis.
Part (b) F(5, 15) = 2.73
Fcrit =
Retain the null hypothesis.
Reject the null hypothesis.
Part (c) F(2, 13) = 3.71
Fcrit =
Retain the null hypothesis....

All questions for problems below is related to one sample
hypotheses test for the population mean.
a) Give the decision rule for rejecting the null hypotheses for
a right tailed test when the significance level is 0.05 and the
sample size is 43.
b) Give the decision rule for rejecting the null hypotheses for
a left tailed test when the significance level is 0.03 and the
sample size is 28.
c) Give the decision rule for rejecting the null hypotheses...

In each part, we have given the significance level and the
P-value for a hypothesis test. For each case determine if the null
hypothesis should be rejected. Write "reject" or "do not reject"
(without quotations).
(a) α=0.01,P=0.06α
answer:
(b) α=0.07,P=0.06α
answer:
(c) α=0.06,P=0.06
answer:

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