Hypothesis Testing & Confidence Intervals

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Hypothesis Testing & Confidence Intervals by Mind Map: Hypothesis Testing &  Confidence Intervals

1. p Value

1.1. What?

1.1.1. p value = P(X-bar >= Sample mean value) under H0

1.2. So What?

1.2.1. Probability of making the Type 1 error

1.2.1.1. Rejecting the H0 when it is TRUE

1.2.2. Used to reject the H 0

1.2.3. Gives indication of statistical significance

1.2.3.1. if statistically strong (5%), reject H0 and Accept H(a)

1.2.3.2. Levels

1.2.3.2.1. <5% (0.05)

1.2.3.2.2. <1% (0.01)

1.2.3.2.3. <10%

1.2.3.3. How to set the level of signicance

1.2.3.3.1. Seriousness of the Type 1 Errors

1.2.3.3.2. Size of remediation/recovery efforts

1.3. Interpretation of the value

2. Hypothesis

2.1. Types

2.1.1. Null Hypothesis

2.1.1.1. What?

2.1.1.1.1. claim that begs evidence AGAINST

2.1.1.1.2. test for "="

2.1.1.2. So What?

2.1.2. Alternative Hypothesis

2.1.2.1. What?

2.1.2.1.1. what we what to prove

2.1.2.1.2. type

2.2. HT Errors

2.2.1. Type 1

2.2.1.1. Reject H0 when it is TRUE

2.2.2. Type 2

2.2.2.1. NOT reject when it FALSE

2.3. Assumptions

2.3.1. Sample is normally distributed (spl, n<30)

2.3.1.1. with μ

2.3.1.2. and σ

3. t-distribution

3.1. What?

3.1.1. another form of normal dist => bell

3.1.2. based on CLT => inference of population based on the sample

3.1.3. T=(x bar - μ) / (s√n)

3.1.3.1. s => sample sd not pop sd

3.1.3.2. s vs σ is the difference

3.1.3.2.1. higher standard deviation then Std.ND => higher spread => higher uncertainty

3.1.4. Excel

3.1.4.1. t > 0

3.1.4.2. Left tailed prob

3.1.4.2.1. T.DIST

3.1.4.3. 2 Tailed prob

3.1.4.3.1. T.DIST.2T

3.1.4.3.2. Always TWICE the value of one sided

3.1.4.4. Right tailed prob

3.1.4.4.1. T.DIST.RT

3.1.4.5. When?

3.1.4.5.1. when done manually, StatTools does it auto.

3.2. Why?

3.2.1. to perform HT for the pop mean μ when pop sd σ is unknown & estimated by sample sd S

3.2.1.1. NO σ NO Z score

3.2.1.1.1. I.e. in practice is Z score is not that useful

3.3. So What (value of T)

3.4. So What (t dist)

3.4.1. when the n<30. t dist. replaces normal dist.

4. From the Class

4.1. Evidence based => p and t values

4.2. Why t. Because you cant use Z without know the pop mean

4.3. T distribution varies based on the degrees of freedom

4.4. Significance level is the probabilty of Type (whats the risk of getting it wrong)

4.5. Need to the def of p value

4.6. if p is low H0 go

4.7. if p is high H0 fly

4.8. Need to do both the manual and stat tools way

4.9. Know how different

5. Unit

5.1. So What

5.1.1. HT => Let the data speak

5.1.1.1. Establish a tentative claim

5.1.1.2. Test the validity of the clain

5.1.1.3. Accept/Reject/Adjust the claim

5.1.2. CI => So what's plausible and how confident are you?

5.2. Outcomes

5.2.1. hypothesis testing jargon in a single sample of data

5.2.2. 2 decision making errors w/ hypotheses

5.2.3. hypothesis test & confidence intervals with μ when σ=given

5.2.4. hypothesis test & confidence intervals with μ when σ=?

5.2.5. interpret(key) p-value, the