Question

Q1. Suppose we wish to test the null hypothesis that a coefficient is equal to zero vs. the alternative that it is not zero at the 5 % level. If the 95% confidence interval for the coefficient does not contain zero, then we will reject the null hypothesis. Explain.

Q2. Suppose we perform an F test and reject the null hypothesis and all the coefficients except the constant are zero. Does this imply the regression is a good fit for the data. Explain.

Q3. Suppose Ŷt = .9857 + .1266 X1 - .088X2 + .7329 Yt-1 (.336) (.0565) (.052) (.1102) (standard errors) R2 = .9958 n = 44 d = 1.11 ρ = .445 Test the Null Hypothesis that there is no first order autocorrelation at the 5% level. (note: with 3 independent variables and 44 observations dL= 1.48 and dU = 1.58 at 5%)

Answer #1

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.

Suppose that in a certain hypothesis test the null hypothesis is
rejected at the .10 level; it is also rejected at the .05 level;
however it cannot be rejected at the .01 level. The most accurate
statement that can be made about the p-value for this test is
that:
p-value = 0.01.
p-value = 0.10.
0.01 < p-value < 0.05.
0.05 < p-value < 0.10.
Complete the sentence: If we do not reject the null hypothesis,
we conclude that _____....

An estimated regression coefficient is equal to 0.5. What is the
confidence level associated with the one sided interval(0.5,∞)?
a. 50%
b. 95%
c. 100%
d. 90%
Suppose a hypothesized slope value is not contained in the 95%
confidence interval. If one were test the hypothesis at the 10%
level which of the following statements are correct?
a. I would reject the null hypothesis
b. I would not reject the null hypothesis
c. I need more information
Suppose the value...

1.Suppose you wish to test the null hypothesis that the mean of
a population is 100 versus the alternative that the mean is not
equal to 100. You then take a sample and calculate a sample of mean
of 90. Which of the following conclusions is correct?
a.
You should reject the null hypothesis
b.
You should not reject the null hypothesis
c.
You should reject the null if n > 30, otherwise do not
reject
d.You should accept the...

3a. Is
there evidence to reject the null hypothesis that the intercept
coefficient is equal to 0 at the 5% level of significance?
(Hint: you will need a table with the t distribution to
determine the critical t.)
3b. Is there evidence to reject
the null hypothesis that the inflation differential coefficient
(Inf h – Inf f) is equal to 1 at the 5% level of significance?
(Hint: you will need a table with the t distribution to
determine...

1a. Suppose the value a is inside the 90% confidence interval
for a coefficient in an estimated regression. Suppose one were to
test the hypothesis that the coefficient is equal to a against the
two sided alternative that it is not equal to a. Which of the
following is a correct statement?
I would not reject the null at the 10% significance level
I would reject the null hypothesis at the 5% level of
significance
I would reject the null...

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

Suppose a random sample of 150 universities is used to test the
null hypothesis that the average number of spam emails economics
graduate students receive in a month is
46.92.The value of the test statistic is found to be 1.02
1. If the null is tested against the alternative hypothesis that
the number of spam emails is not 46.92, the smallest significance
level at which you can reject the null hypothesis is.
2. If the null is tested against the...

1. Suppose we are conducting a left tailed hypothesis test and
find zobs = −3.23.
a. Find the p-value.
b. If we are conducting the test at the 5% level of
significance, would we reject or fail to reject Ho?

Suppose OLS assumptions A1-A4 hold and we want to test the joint
null hypothesis that β 1 = β 2 = 0. We obtain the t-statistics t1
and t2 for the single null hypothesis that β 1 = β 2 = 0
respectively. Further denote C alpha/2 as the critical value that
satisfies P(|N(0;1)|> C alpha/2) = Alpha/2, where N(0,1) is the
standard normal. Our rule is if one of the two t-statistics is
greater than C alpha/2, we will...

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