Estimation and Confidence Intervals Flashcards
What is a point estimate?
The point estimate is a single value, which is the best estimate of the parameter of interest.
They always contain an element of doubt.
What is an interval estimate?
What is the difference between small and large samples?
The interval estimate is a range of values that give an idea of the likely accuracy of the estimate.
A small sample will have a large interval.
A large sample will have a small interval.
What is an estimator?
Give an example of an estimator of the population mean.
An estimator is a rule or set of rules that describes how to derive the estimate of the parameter from the sample data.
Possible estimators of the population mean:
1) Sample mean
What can be said about an unbiased estimator?
An estimator is said to be unbiased if its expected value is equal to the parameter being estimated.
An unbiased estimator does not guarantee that a single use of the estimator will yield a correct estimate of the parameter.
What is precision?
Precision is a relative concept comparing one estimator to another.
Estimator A more precise than estimator B if the estimates it yields are less spread out than the estimates generated by B.
One estimator is more precise than the other if it has a lower variance.
What is the mean squared error of the estimate?
The mean-squared error of the estimate combines bias and precision.
What is a confidence interval?
How is the 90% confidence interval calculated?
If we took many samples from a population with mean, μ and calculated a confidence interval from each sample, we would find that μ lies within 95% of the calculated intervals.
The 90% confidence interval is calculated by finding the z-score which cuts off the outer 10% of the normal distribution.
The greater the degree of confidence required, the wider the interval has to be.
When is t-distribution used?
The t-distribution can be used if the population is normally distributed and when variance is unknown. Or if the population is not normally distributed but the sample size is large, however variance is still unknown.
