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)