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ECO 3411 Exam 2 terms #2
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Terms in this set (52)
A hypothesis is
A statement that can be subjected to empirical evidence.
A theory
Is a hypothesis that is found consistent with empirical evidence
Alternative Hypothesis (HA)
The condition the test is trying to establish
Null Hypothesis (H0)
The state we wish to reject
All possible conditions of the unknown population are reduced to one of two states
Null Hypothesis (H0) & Alternative Hypothesis (HA)
Reject H0 allows us to
Accept HA
Testing attempts to
determine whether these parameters have particular hypothesized values
HA & H0 are mutually
Eclusive and Exhaustive events by defining the null hypothesis as the complement of the alternative hypothesis
A one-sided test is
required to test an alternative hypothesis containing a one-way inequality either strictly greater than or less than
Two-Sided test
A not-equal sign in HA directs us
H0 & HA refer to
the unknown population parameters, not their sample estimators
Type I error
If we reject the null hypothesis when in fact the H0 is the true state of nature for the population
Type II Error
Failure to reject H0 when HA is true for the population
In Hypothesis testing, a is
the probability of committing a type I error
In Hypothesis testing, B is
The probablity of comiiting type II error
The smaller the value we assign to a,
The larger will be the B, and vice versa
By assigning value to a,
We automatically determine B
Although usually unknown, B
may be reduced by adopting a larger a or increasing the sample size
The significance level is
The probablilty of type I error, a
Inequality in HA is considered
Statistically significant if the test results in rejection of H0
If H0 cannot be rejected at the a significance level,
Then the expression described by HA is not statisically significant
A decision rule for a test
is the criteria for rejecting or not rejecting the null hypothesis
A test statisitc
is a random variable constructed from sample information and the assumption that the null hypothesis is true
A rejection region is
the range of test statistic values improbable enough to reject the null hypothesis at the a level of significance
Decision rules using Test Statistics:
We reject H0 if the test statistic lies within the Rejection region. Otherwise we can not reject H0
A p-value decision rule is equivalent
to the corresponding test statistics decisions rule and the p-value rule is usually more flexible and easier to use
In estimation, the mean of the sampling distribution is
the value for the estimator of the unknown parameter
In testing, the mean of the sampling distribution is
the hypothesized value of the parameter specified in the null hypothesis
Z-Statistic
(X Bar- u0)/ Stand. Dev.
t-statistic
(X Bar- u0)/s
Z-statistic & t-statistic
are the test statistics for the population mean from samples with known and unknown standard deviations
The Z-statistic & t-statistic for one-sample mean tests measures
How many standard errors X Bar is from the null hypothesized value of u0
Statistical significance requires
A persistent pattern in a small sample data
If considerable dispersion exists in statistical significane in the population
larger samples should be selected
For paired data
one-sample tests are used to test the difference in population means
Statistical significance of an explanatory variable is
established by rejecting the null hypothesis that the variable's coefficient is zero in the population equation
If an explanatory variable is significant by a two-sided test,
-a postive sample regression coefficient indicates a significant, DIRECT relationship with the dependent variable
- A negative coeffificent indicates a significant, INVERSE relationship
A one-sided test of an explanatory variable is justified
only if one possible direction of the relationship can be disregarded
Altering an alternative hypothesis to accomodate an unexpected coefficient sign in the sample regression is
unethical
Significance tests involving B0 are usually
not too informative or statistically reliable
Design regression model to include all important explanatory varaibles
Step 1 for procedure for Inferences about Explanatory variables
Decide which variables to test and whcih to include merely as control variables
Step 2 for procedure for Inferences about Explanatory variables
Determine whcih variables are eligible for one-tailed tests and in which direction
Step 3 for procedure for Inferences about Explanatory variables
Assign a by your willingness to be wrong when you claim a variable is significant
Step 4 for procedure for Inferences about Explanatory variables
Collect the largest possible random sample within resource limits of the study
Step 5 for procedure for Inferences about Explanatory variables
Use p-value decision rule to conduct tests, by use p/2 to conduct one-tailed tests
Step 6 for procedure for Inferences about Explanatory variables
Translate test results into verbal conclusions about whcih variables test significant
Step 7 for procedure for Inferences about Explanatory variables
Find interval estimates for sginificant variables and interpret as marginal effects
Step 8 for procedure for Inferences about Explanatory variables
If an explanatory variable does not test significant
its marginal effect on the dependent variable should not be estimated
Practical significance is
reflected by the marginal effect of a typical change in the explanatory variable
The significance level of explanatory variables tests becomes diluted if
additional variables are tested from the same regression
A wide ranging explanatory variable and a large sample
gives a weak relationship its best change to test significant
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