Week 2 Flashcards
What is statistics used for?
Statistics are crucial for learning about the population of interest using a random sample from the population
What is estimation?
Estimation is computing a ‘best guess’ numerical value for an unknown characteristic of a population distribution from a sample of data
What is inference?
Inference is making a decision about the set of parameter values which is reasonable for the parameters of the population
What is an estimator?
Estimator is a function of a random sample that takes values in the parameter space
What is an estimand?
Estimand is a non random feature of the population.
What is an estimate
Estimate is the realized value of the estimator for the particular random sample at hand.
What is the formula for sample average?
When is an estimator unbiased?
If we have 2 unbiased estimators, which one of them is more efficient, the one that has less variance or more variance?
Less
When is an estimator consistent?
When is sampling average an unbiased estimator for population mean?
What does sample mean being BLUE mean? and what does sample mean minimise?
What are the 2 reasons that differences between sample averages and hypothesized value may arise?
In large samples due to CLT, what is an approximation for a normal distribution?
What is the formula for an estimator of a sample variance?
What is the estimator of the standard deviation of Y called and what is it’s formula?
What is the formula for t-stat?
With large random sample due to CLT the t-stat is approximately same as what distribution?
Normal
At the 5% Significance level, what is the decision if t-stat is greater than 1.96
Reject
If t-stat is greater than 1.96, the population mean is ?
Statistically Significant at the 5% significance level
What are the 2 errors in hypothesis testing
- Ho is True but we reject Ho (Type 1)
- Ho is False but we fail to reject Ho (Type 2)
How to test a hypothesis about the population using a large random sample from population
- State hypothesis
- Calculate the t-stat
- Reject if t-stat is greater than critical value
When do we reject p-value
If p-value is less than significance level
What is the formula for a 95% confidence interval?
What does a confidence interval tell us?
A confidence interval tells us for the confidence level of the intervals, would contain the true value ‘however many % of the confidence level’ of the random samples.
write hypothesis test if the average earnings of men and women is different.
For the hypothesis test if the average earnings of men and women is different, write the estimator of the sample mean according to CLT.
For the hypothesis test if the average earnings of men and women is different, what is the standard deviation formula?
For the hypothesis test if the average earnings of men and women is different, what is the standard error formula?
For the hypothesis test if the average earnings of men and women is different, what is the t-stat formula?
For the hypothesis test if the average earnings of men and women is different, what is the 95% confidence interval?
What is the formula for sample covariance?
What is the formula for sample correlation coefficient?
