Hypothesis Test

Front 1

What is hypothesis?

Back 1

It is an assumption that we assume to be true.

Front 2

What is hypothesis testing?

Back 2

Use to make inference about the parameter from statistics.

We will assume our guess for population parameter to be true (i.e. H0), and then use sampling statistics to determine if we have enough statistical evidence to reject H0 or not.

Front 3

H0

Back 3

assumption about the parameter = value we set for population

Front 4

H1

Back 4

Alternative hypothesis:
we want to see if the value we set for population is actually larger, or smaller, or not equal than we set.

Front 5

Type 1 error = alpha

Back 5

This is the error when we reject H0 but actually H0 is true

Front 6

Type 2 error = beta

Back 6

This is the error when we not reject H0 but actually H0 is false

Front 7

Table of Hypothese error

Back 7

xxxxxx H0 = true | H0 = false
xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Reject | type 1 | correct
xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
!Reject| correct | type 2
xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Front 8

Two Actions

Back 8

- Reject H0,
- Or not reject H0

Front 9

Two conclusions

Back 9

- We have enough evidence to support H1 => reject H0
- We doesn't have enough evidence to support H1=>!Rej

*Note: we can't say we accept H0 is right

Front 10

Procedure of hypothese testing

Back 10

(1) Two hypothese: H0, H1
(2) Assume H0 is true
(3) Find evidence to support or not support H1
(4) Two actions: rej H0/ !H0
(5) Two errors: P(type 1)=alpha, P(type 2) = beta

Front 11

When to reject H0? in what degree?

Back 11

(1) Given the distribution with H0 is true
(2) within the distribution, we want to find out the region of rejection and no rejection.
(3) Since in the dist., we assume H0 is true. If we reject, we will commit the type 1 error.
(4) Thus, the point that we find at where we commit type 1 error is the point which seperate the reject and accept regions.
(5) If the value [test statistics] in our sample is in the reject region, then it means we have committed type 1 error given that H0 is true; thus, we have enough evidence that H0 should be rejected.

Front 12

Rejection region

Back 12

Is a range in H0 = true distribution that if our test statistics falls into this region, we should reject H0.