52 terms

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 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