Inferential Statistics Flashcards
What are the properties of the sample mean for random variables?
- Mean/E(x) = population mean
- Variance equal pop variance/n
- Based on the CLT, its distribution can be approximated to a normal/Gaussian one
What are the properties of the sample proportion for random variables?
- Mean=p
- Var = p(1-p)/n
- Based on the CLT, its distribution can be approximated to a normal/Gaussian one
Is the sample mean an unbiased and consistent estimator for the population mean?
Yes
What does the sample standard error shows us?
It’s an approximation of the overall error we make when estimating the population mean using the sample mean (S/sqrt(n)
What doe as (1-a)100% confidence interval show us?
We are (1-a)100% sure the unknown parameter (mean) belongs to it
What happens to an interval length as the variance increases?
The higher the se, and thus the wider the length will be
What happens to an interval length as the sample size increases?
The lower the se, and thus the shorter the interval
What happens to an interval length as the confidence level increases?
The greater the t or z value will be, thus the wider the interval will be
How many degree of freedom does a student t distribution has?
n-1
What happens to the distribution as the degree of freedom increases?
The more similar to a normal distribution it will be
What is the se of probability?
sqrt{p(1-p)/n}
What do we want to asses in hypothesis testing?
We want to know if there is enough empirical evidence against Ho and in favor of H1. Ho is assumed to be true
What is type I error?
rejecting Ho when it is true
What is type II error?
Rejecting Ho when not true
Which one is the worst type of error?
Type I, because Ho is indeed describing the current situation, and by rejecting it we will incur costs that don’t need to be afforderd
What happens when we commit type II error?
Nothing, no action is taken and thus no costs are incured
What does a significance test of level a means?
That the probability of making type I error is of a
When do we reject Ho based on the p-value?
When its value is lower than a
What does the p-value return us?
The probability of observing a value of the sample mean
What are asymptotic tests?
When we cannot rely on the normal distribution, thus we use estimators. We use the z value
How many degrees of freedom for hypothesis testing on 2 variables?
NX+NY-2
