Statistical Inference, Estimation and Hypothesis testing Flashcards
Define: Null hypothesis
Define: Confidence interval
95% sure that true parameter lies within calculated interval; 1- α
Define: Level of significance
probability of committing a type I error.
Define: Acceptance region
Define: Test Statistic
Define: Critical Value
The lower and upper limits of the acceptance region
Define: Statistical Inference
the study of the relationship between a population and a sample drawn from that population.
What is the first step in Statistical Inference?
Estimation
Define: Point Estimation
estimates the population parameter with one numerical value (X).
Define: Type I error
the error of rejecting a hypothesis when it is true.
Define: Type II error
the error of accepting a false hypothesis.
List: Properties of Point Estimators
- Linearity
- Unbiasedness
- Minimum variance
- Efficiency
- Best linear unbiased estimator (BLUE)
- Consistency
Explain: Linearity
The estimator is a linear function of the sample observations.
Explain: Unbiasedness
If in repeated application of the method the value of the estimators coincides with the true parameter value.
Explain: Minimum variance
If its variance is smaller than that of any other estimator of the parameter value.
Explain: Efficiency
If only unbiased estimators of a parameter are considered, the one with the smallest variance is efficient.
Explain: Best Linear Unbiased Estimator (BLUE)
If the estimator is linear, unbiased and has minimum variance in the class of all linear unbiased estimators.
Explain: Consistency
If the estimator approaches the true value of the parameter as the sample size increases.
