H2) Two-Sample t-Test in Python

A1) Mutually Exclusive vs Independent Events

A2) Conditional Probability Formula for Independent Events

A3) Law of Large Numbers (LLN)

A4) If you test positive for cancer, what is the probability that you in fact has cancer?

A5) Are Disjoint Events Independent?

B1) What is a Random Variable?

B2) Expected Value of a Random Variable

B3) Random Variable: Variance and Standard Deviation

B4) Prove that E(cX) = cE(X)

B5) Prove that Var(cX)=ccVar(X)

B6) Var(X)=E(X^2)-[E(X)]^2

B7) Bernoulli Random Variable

C1) Random Variables: Mean and Standard Deviation

C2) Covariance vs Variance

C3) Correlation vs Covariance

C4) Cov(X,Y)=E(XY)-E(X)E(Y)

C5) If X and Y are independent, then Cov(X,Y)=0

C6) Var(X+Y)=Var(X)+Var(Y)+2Cov(X,Y)

D1) Standard Normal Distribution

D2) What is z-score?

D3) What means independent and identically distributed (iid)?

D4) Central Limit Theorem (CLT)

E1) Population Parameter vs Sample Statistic

E2) Standard Error of the Mean

E3) Random Sample

E4) Unbiased Estimator

F1) 95% Confidence Interval for Proportion (p)

F2) Normal vs Student’s t-distribution

F3) Confidence Interval for a Population Mean

F4) Margin of Error

G1) Null vs Alternative Hypothesis

G2) Type I vs Type II Errors

G3) Z-test for a Proportion

G4) T-test for the Mean

H1) Randomized Experiment

H2) Two-Sample t-Test in Python

H3) Two-Sample z-Test in Python

[fayezsalame]

Very informative video. Better than the explanation in the books. It is refreshing to find a way to conduct these tests so easily without having to write it down over and over again on a piece of paper.

[davidcriss]

I found the two-tail test (and explanation of the math) you discuss in this video to be very helpful for one of the questions on Lab #2. Thank you

[tellmesomethingsweet]

In lab 1 we had an exercise in which we used the z-statistics to determine if the proportion of International Masters that stopped at node 3 is equal to the proportion of other chess players that stopped at node 3 of the centipede game. With lab 2 we used Two-Sample t-Test and I'm a bit confused as to which test is more appropriate in which situations. Also, the video is very clear and straightforward, thank you so much!

[kayleighjames]

Very helpful for Lab 2, thank you for the clear explanation!

[clevelandgabby]

this has helped me in lab 2. I now fully understand the two-tail test.

[lanciauxrayzimba]

Thanks a lot for the video. I have some questions:
1. Are the sample sizes equal for each group? (how many sample sizes for white and how many sample sizes for black?
2. Do you not need to check if the data is normally distributed? Does it matter?

[yahiaabdelbar]

Why in the experimental study it is ok to examine the difference between sample means without the necessity of running a formal test?

[djhass]

what about compare 3 classes, t-test method will help in this situation?