ECON 220

is a sample statistic U used to provide a one-point approximation to the value of an unknown parameter θ.

is given by the absolute value of the difference between the estimated value and true value of the parameter of interest.

| U-θ |

Geometrically: Sampling error measures the distance between the two points U and θ.

U attempting to estimate θ such that E(U) = θ.

E(U) - θ

Suppose U and W are two unbiased estimators for θ. Then U is ___________ provided that it has a smaller variance.

• of U to W:
• 100[V(W)/V(U)]

the percentage 100(1-α)%

Sample Mean ± Critical Value * Standard Error

• limit on the size of sampling error.
• P(sampling error<MOE)= 1-α

• Normal Population
• VSRS
• σ is known

xbar ± Z_α/2 (σ/√n)

Under repeated random sampling, the statistical procedure yeilds an interval containing the true value Θ of the parameter of interest 100(1-α)% of the time.

• VSRS
• n is sufficiently large (ie: n is greater than 30)
• σ is unknown

xbar ± Z_α/2 (s/√n)

have fatter tails than normal curves

df/(df-2)

is greater than 1 but convergys to 1 as df-->infinity

standard normal distribution as df-->infinity

• VSRS
• normal population
• σ is unknown

xbar ± t_α/2 (s/√n)

• Binomial Population
• VSRS
• n is sufficiently large (np≥5, n(1-p)≥5)

pbar ± Z_α/2 (√pbar(1-pbar)/n)

statement about the population of interest.

statement about the populatin of interest that contradicts the null hypothesis.

sample statistic that is used to summarize the evidence.

probability of making an error in judgement.

(Heuristic) The P-value is the probability of observing a value of the test statistic "at least as extreme as" what was actually observed.

-focuses on type I error (false positive)

the P-velue is computed by temporarily assuming the null hypothesis is true.

a low P-value casts doubt upon the assumption that the null hypothesis is true. Thus, we reject it.

a high P-value is consistent with the assumption that the null hypothesis is true. Thus, we do not reject it.

power calculations

the p-value is the smallest significance level for which the null hypothesis can be rejected.

false positive

false negative

specifies the set of values of the test statistic for which the null hypothesis is rejected in favor of the alternative hypothesis and the set of values for which the null hypothesis is accepted.

consists of all values of the test statistic for which the null hypothesis is rejected.

consists of all values of the test statistic for which the null hypothesis is accepted.

value that separates the rejection region from the acceptance region.

1-B where B is the probability of making type II error

• Binomial Population
• VSRS
• n is sufficiently large (based on null hypothesis value of p)

z=pbar-pnot/(√pnot(1-pnot)/n)

• probability of observing a value of the test statistic "at least as extreme as" what was actually observed.
• the p-value is the smallest significance level for which the null hypothesis can be rejected.
• **p-value is the observed significance level**

positive square root of R Square. Large value indicates a good fit.

number indicates that ___% of the variation in the response variable Y is explained by its linear relationship with the explanatory variable X.

adjustement of R Square for degrees of freedom. The adjustment serves as a penalty for using too many explanatory variables.

"Standard Error of Regression" and estimates the standard deviation of the error specification in the model. A relatively small standard error is another indication of a good fit.

"Regression" always refers to the part that is explained and "Residual" to the part that is unexplained. The "Total" is typically the sum of the explained and unexplained components, wherever this way of thinking is useful.

analyzes degrees of freedom. The total degrees of freedom is always n-1. If there is only one explanatory variable, Regression df=1. The Residual degrees of freedom is what is left over (ie: 19-1=18).

analyzes the variation in the response variable in terms of Sum of Squares. The Total Sum of Squares is simply the sum of the squared deviations from the sample mean for Y. The Regression SS is the variation in the response variable Y that is explained byt he regression line. Residual SS is interpreted as the variation in the response variable Y that is not explained by the linear regression line.

Mean Square is a Sum of Squares divided by the appropriate degrees of freedom. It is easy to check that the square root of the Residual MS is equal to the Standard Error of Regression listed in the Regression Statistics.

F-Statistic is the ratio of MS Regression to MS Residual. Large value of F supports the alternative hypothesis that the linear regression model fits the data against the null hypothesis that the linear regression model does not fit the data.