Lecture 2 Flashcards
Parameters
describe the population e.g. population mean (mu_x), population variance (sigma^2) & population standard deviation (sigma)
Statistics
infer the population e.g. sample mean (Xbar), sample variance (s^2) & sample standard deviation (s)
What is a reasonable point estimate of the population mean?
sample mean
How do we quantify the level of uncertainty of the point estimate (Xbar)?
interval estimation e.g. confidence level/confidence interval
How do we figure out the sampling distribution of the point estimate (Xbar) to construct interval estimates?
central limit theorem
What does the central limit theorem (CLT) tell us & what are its applications?
it tells us the distribution of our estimator & is used for hypothesis testing and to build confidence intervals
What is a confidence interval & what is its formula?
it gives a range of values (e.g. [09, 14]) that is intended to cover the parameter of interest to a certain degree of confidence [insert image]
What is the difference between standard deviation and standard error?
TBA
review slide 9
in lecture 2 on ipad
Confidence interval interpretation
we expect 95% of these interval to cover the true population mean (mu_x) and 5% do not
The length of a confidence interval (CI) reflects…
our estimation uncertainty
What does the length of a CI depend on?
population standard deviation (sigma), confidence level (1 - alpha) & sample size (n)
review slide 18 & 19
in lecture 2 on ipad
In practice, it is unlikely that sigma (population standard deviation) is available to us, what is reasonable solution to this dilema?
replace sigma with s (sample standard deviation)
When using s instead of sigma how do we account for the added uncertainty?
use a slightly different sampling distribution that has fatter tails (student’s t distribution) [insert image]
review slide 23
in lecture 2 on ipad
What is hypothesis testing?
a method for using sample data to decide between 2 competing claims (hypothesis) about a population characteristic/parameter (e.g. mu)
Null hypothesis
H_0, a claim about a parameter that is initially assumed to be true
Alternative hypothesis
H_a, the competing claim
What are the only 2 possible decisions in a hypothesis test?
reject H_0 & fail to reject H_0
A statistical hypothesis test is only capable of demonstrating strong support for…
the alternative hypothesis, so be careful when setting up hypothesis
What does rejecting the H_0 indicate?
strong support for the alternative hypothesis, H_a
What does failing to reject the H_0 indicate?
lack of strong evidence against the null hypothesis, H_0
Type I error
denoted by alpha, is when we reject H_0 even though H_0 is true
Type II error
denoted by beta, is when we fail to reject H_0 even though H_0 is false
A test statistic incorporates…
the sample size (n), the point estimate (Xbar), the standard deviation (s) & the hypothesized value (mu_0)
