Exam 1

The formula for the sample mean is

(1/n) Sigma Y

What does it mean when you calculate a 95% confidence interval

-95% confident -5% chance of error -95% of the time the parameter will be captured

Y = B0 + B1X + E

-BO and B1 are parameters -B0 is starting point and B1 tells us how far the parameters go -E is our disturbance term -X is the variable from our data that has the effect on Y -Y shows the relationship between X and Y

econometric triangle

-specific research question -input data into econometric analysis to create empirical model -hypothesis helps you derive your model and also tells you what data yo will be testing

falsify

Falsify means that we have to find just one case that contradicts a statement or hypothesis or conjecture

Verify

Verify means we have to show that a statement or hypothesis or conjecture is true for all cases

Which of the following is a correct statement to make about a null hypothesis when the p-value is less than 0.05?

We can reject the null hypothesis on the basis of the sample evidence

The reproductive property of normals states that

a linear combination of normals is normal.

A parameter is a known constant of the population.

false

In the subject of statistics, our primary focus is on determining the value of statistics

false

Statistical hypothesis testing is concerned with arriving at simple yes/no decisions regarding the value of a population parameter

false

Statistics is the science of problem solving in the presence of random data variability

false

The alternative hypothesis is the one actually rejected or not rejected based on the outcome of a test.

false

The mean of a sample mean is the true population mean

false

The null hypothesis is a statement or conjecture that always involves an inequality sign.

false

An estimator is the value obtained from a formula or procedure

false. An estimator is the formula. An estimate is the value derived from the estimator.

A Type I error is the rejection of the null hypothesis when the alternative is true.

false. Type 1 error is when you reject the null when it is in fact true

A confidence interval is constructed using a test statistic such as Z.

false. Z is not a test stat.

In point estimation, a single interval is used as the best guess of a population parameter.

false. a single value is used, not a single interval

The population mean for a discrete random variable Y is found using the following formula: (1/n)SIGMA y

false. this is the sample mean.

A Type II error is the rejection of the null hypothesis when in fact it is true.

false. type 2 error is not rejecting the null when it is false.

An estimator, theta(hat), of a population parameter is unbiased if

if e (theta hat) = theta

What would happen (other things equal) to a confidence interval if you calculated a 99% confidence interval rather than a 95% confidence interval?

it should be wider

A _______ is a numerical characteristic of a sample and a _____ is a numerical characteristic of a population

parameter, statistic

The formula for the sample variance is

s^2= 1/(n-1) Sigma (Y-Mu)^2

econometrics

the application of a specific method to the general field of economics in effort to falsify theorem

A central problem with data is that they are subject to random variation

true

A confidence interval is a probability statement asserting the likelihood that the interval contains the true population parameter.

true

A parameter is a numeric characteristic of the population

true

A population consists of all possible items or units possessing one or more common characteristics under specified experimental or observational conditions

true

A random variable is a variable whose value is not known until it is observed as the result of an experiment or an observational study

true

A sample is a subset of a population.

true

A simple random sample (SRS) of size n is one in which every sample of size n has an equal chance of being selected as the sample.

true

A statistic is a formula calculable with data

true

A statistic is a numeric characteristic of a sample calculated from sample data.

true

Each null hypothesis must have a corresponding alternative hypothesis.

true

One possible source of random data variability is pure differences between the units being studied.

true

Random data variability is due to unknown and unknowable causes

true

Since a parameter is unknown by definition, we must use some procedure to infer the value of the parameter

true

The Central Limit Theorem states that, no matter what the underlying distribution of a random variable, the distribution of the sample mean will be normal as the sample size gets larger.

true

The formal definition of the expected value of a discrete P random variable Y is: E(Y ) = SIGMA yp(y)

true

The population variance for a discrete random variable Y is found using the following formula: v(y)= sigma ^2 v(y)= E[Y-E(Y)]^2

true

The probability of rejecting the null hypothesis when in fact it is false is called the significance level of the test.

true

The rejection of the null hypothesis when in fact it is false is not an error.

true

The t-distribution used for confidence interval construction and hypothesis testing has n -1 degrees of freedom, where n is small.

true

The true population parameter is either in a single interval calculated from sample data or it is not.

true

if y~N (mu, sigma^2), then mu(y bar) is the overall population mean of Y

true

Rejecting the null hypothesis when it is true is called a

type 1 error

__________ results if you fail to reject the null hypothesis when the null hypothesis is actually false.

type 2 error

Which of the following is a correct statement to make about a null hypothesis when the value of the test statistic is within the range of the critical value?

we only reject null when outside of the range

If Y~ N then for Y

z= (y- m)/ (sigma/sqrtN)