Question

Suppose we fit a VAR model to 6 time series simultaneously. At the 0.05 significance level, a 0.03 p-value of the Jarque-Bera test means that:

a) The constant variance assumption is not violated

b) The normality assumption is not violated

c) The normality assumption is violated

d) The constant variance assumption is violated

Answer #1

Solution:

Consider the Jarque-Bera test . It is a goodness of fit test.

The null hypothesis of this test is stated as

H_{0} : The data in each mix design comes from a normal
distribution with unknown mean and variance.

i.e. There is the normality assumption in the null hypothesis.

Here in the given test , p value = 0.03

= 0.05 ..significance level

p value is less than significance level

The
**null hypothesis is rejected** at 0.05 significance
level.

**The
normality assumption is violated.**

**Option c is correct**

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

4. When doing a significance test, an investigator obtained a
p-value of 0.1. You may assume a significance level of 0.05. This
means that:
A. Assuming Ho is true, this sample’s result was an unlikely
event.
B. Assuming Ha is true, this sample’s result was an unlikely
event.
C. The data are consistent with H0.
3. A one-way ANOVA analysis is run with 4 different factor
levels where the normality assumption is not met. The p-value of
the F-test is...

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.

Conduct the following test at the a = 0.05 level of significance
by determining (a) the null and alternative hypotheses (b) the test
statistic (c) the critical value (d) the P-value. Assume that the
samples were obtained independently using simple random sampling.
Test whether p1 does not equal p2. Sample data are x1 = 30, n1=254,
x2 =38 and n2 =302.

Suppose that in a multiple regression the overall model is
significant, but the p values of none of the individual slope
coefficients are small enough. This means that:
a.none of the other choices are correct
b. nonlinear model would be a better fit
c. the assumptions have been violated
d. multicollinearity may be present
e. linear regression would be better

Suppose we want to test the null hypothesis H0 : p = 0.28
against the alternative hypothesis H1 : p ≠ 0.28. Suppose also that
we observed 100 successes in a random sample of 400 subjects and
the level of significance is 0.05. What is the p-value for this
test?
a. 0.9563
b. 0.0901
c. 0.05
d. 0.1802

Statistical significance (alpha level;
p-value) reflects the odds that
a particular finding could have
occurred by chance.
If the
p-value for a difference between
two groups is 0.05, it would be expected to occur by chance just 5
times out of 100 (thus, it is likely to be a “real” difference). We
define a p-value of less than 0.05 to indicate statistical
significance.
Suppose a pizza place claims their delivery times are 30 minutes
or less on average but you...

1. Choose the correct statistical decision at the 0.05
significance level based on the given research finding.
A researcher measured the amount of relationship as “4.68” from
the normal distribution with mean = 2 and standard deviation =
1.
A. The observed sample relationship is inside the critical
region. B. The observed sample relationship is outside the critical
region. C. We need more information to decide.
D. There is no significant relationship
2. When the p-value is observed as 0.014,...

1) When we fit a model to data, which is typically larger?
a) Test Error b) Training Error
2) What are reasons why test error could be LESS than training
error? (Pick all that applies)
a) By chance, the test set has easier cases than the training
set.
b) The model is highly complex, so training error systematically
overestimates test error
c) The model is not very complex, so training error
systematically overestimates test error
3) Suppose we want to...

Conduct a test at the a= 0.05 level of significance by
determining (a) the null and alternative hypotheses, (b) the
test statistic, and (c) the P-value. Assume the samples were
obtained independently from a large population using simple random
sampling.Test whether p1 >p2. The sample data are x1=121,
n1=258, x2=144, n2=317
B. Determine the Test Statistic. z0= ? (Round to two decimal
places).
C. Determine the P-Value = ? (Round to Three Decimal
Places).
Please label answers B & C...

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