Week 3 - Hypothesis testing

Question 1

Hypothesis

Answer 1

Clear statement about the population distribution

Question 2

Parametric hypothesis

Answer 2

Statement about the parameters of the population distribution

Question 3

Null hypothesis

Answer 3

A hypothesis that specifies ‘no effect’ or ‘no change’

Denoted as H₀

We need to show there is sufficient evidence against
the null hypothesis

Question 4

Alternative hypothesis

Answer 4

A hypothesis that specifies the effect of interest

Denoted as H1

Question 5

Simple hypothesis

Answer 5

Specifies only one value for the parameter(s)

H₀ = 0.06

Question 6

Composite hypothesis

Answer 6

Specifies many possible values

H1 < 0.06

Question 7

Statistical test

Answer 7

A decision rule for deciding between H₀ and H1

Question 8

Test statistic

Answer 8

‘T’ - is a statistic on which the test is based

Question 9

Decision rule

Answer 9

reject H₀ if T ∈ A

Question 10

Critical region

Answer 10

Known as Set A

If it is an interval, the boundary value is called the critical value

Example
- The test statistic is Y.
- The decision rule is to reject H₀ if Y <= 7.
- The critical region is (−∞, 7].
- The critical value is 7.
- If Y is less than or equal to 7, reject null, otherwise there is not enough evidence to reject null

Question 11

Type 1 Error

Answer 11

when a null hypothesis (H₀) is incorrectly rejected, even though it is true

Question 12

Type 2 Error

Answer 12

when the null hypothesis (H₀) is incorrectly accepted, even though it is false

Question 13

Significance Level

Answer 13

(denoted by α) is the threshold used in hypothesis testing to determine whether to reject the null hypothesis (H₀)

Usually α is 0.05, and we will use the p-value to determine if surpass α or not

Question 14

P-value

Answer 14

Probability of observing data that is, as, or more extreme than what was actually observed

Decision rule: reject H0 if the p-value is less than the significance level

When working with two-sided test, double probability of one tail

Question 15

Hypothesis - Single Mean

Answer 15

T-test -> T = (X¯ - u)/(S/√n) ~ tn−1

Question 16

Simulation

Answer 16

Work out distribution model you assume -> get pc to simulate from it (since you have no data) -> get estimate of sampling distribution -> can use to get the p-value

simulation technique works even when the CLT does not

Question 17

Permutation Test

Answer 17

Gender and promotion case study

• If gender does not play a role, that means each person has equal chance of getting promoted
• Using simulation, we can swap males and females around then calculate test statistic of difference between the males and females
• Then ultimately compare between the original to see if the p-value got as high as the data result