Week 5 - Foundations for inference

Question 1

sampling variability

Answer 1

our point estimate isn’t exactly equal to p

Question 2

bias

Answer 2

we may systematically under or over estimate the true value

Question 3

central limit theorem

Answer 3

as the sample size grows, the distribution of the sample proportion can be approximated by a normal distribution

Question 4

hypothesis testing

Answer 4

another way of conducting statistical inference - a formal way of pitting 2 mutually exclusive statements against each other

Question 5

2 hypothesis statements

Answer 5

Null hypothesis - there is nothing going on
- defendant is innocent
Alternative hypothesis - there is something going on
- defendant is guilty

general rule - null is true until we prove otherwise, but we never accept the null hypothesis

Question 6

one sided hypothesis test vs two sided

Answer 6

one sided = only checking for an effect in one direction
two sided =

Question 7

significance level

Answer 7

this defines the threshold p value below which the null hypothesis will be rejected 0.05 is the most common

Question 8

the null distribution

Answer 8

the distribution of possible outcomes under the null hypothesis

Question 9

type 1 error

Answer 9

when we reject a null hypothesis that is true
the probability of a type 1 error is denoted by ‘a’
when the null is true 100 x a% of the time you will observe a p value below ‘a’

Question 10

type 2 error

Answer 10

when we fail to reject a false null hypothesis

the probability of making a type 2 error is denoted by BETA

Question 11

significance level

Answer 11

the probability that the event could have happened by chance
the probability of rejecting the null when its actually true

Question 12

margin of error

Answer 12

the range of values around the sample statistic that is likely to contain the true population parameter

Question 13

chi square goodness of fit test

Answer 13

used to determine if the data in your sample is drawn from some hypothesized distribution. ie does your expected response match the actual response.

Question 14

chi square considerations

Answer 14

independence
at least 2 degrees of freedom
at least 5 values in each category it think

Question 15

the t distribution

Answer 15

the t distribution is used when we aren’t given the standard deviation. it accounts for the extra uncertainty of another estimated value.

its very similar to the normal distribution but is more spread out to reflect the uncertainty

Question 16

t distribution and degrees of freedom

Answer 16

it has one parameter - DF
as df increases, the t distribution becomes less spread out and eventually approximates to the standard normal distribution