Hypothesis Testing IV

Lecture 24

Dr. Elijah Meyer

Duke University
STA 199 - Spring 2023

April 12th, 2023

Checklist

– Clone ae-23

– Peer Review Lab Due Today (April 12th)

– HW-6 (Statistics Experience) due April 28th

– Project Final Report (April 28th)

– Project Presentations (April 25th)

– HW 5 Due Thursday (April 13th)

– Second Peer Evaluation (April 14th by 5:00 PM)

– Exam 2 starts April 14th at 5:00 PM

– Good Conversation in Slack! Check it out

R Error Announcements

– Error: To many files

This is not your fault

Homework Announcements

– Homework 4 Question 7

– Homework 5 Population Median

— There is no widely accepted standard notation for the median

— \(\eta\)

— \(\mu\) and define correctly

— sample median x̃

Homework Announcements

– Homework 5 Question 2

— Single mean

— Air bnb example

Last Time (and continued today)

– \(\mu\) -> \(\pi\)

– \(\mu_1 - \mu_2\) -> \(\pi_1 - \pi_2\)

– \(\bar{x_1} - \bar{x_2}\) -> \(\hat{p_1} - \hat{p_2}\)

Context (CPR)

Here we consider an experiment with patients who underwent CPR for a heart attack and were subsequently admitted to a hospital. Each patient was randomly assigned to either receive a blood thinner (treatment group) or not receive a blood thinner (control group). The outcome variable of interest was whether the patient survived for at least 24 hours, and the researchers are interested in if giving a patient the blood thinner impacts the outcome of survival.

Explanatory Variable -

Response Variable -

Null Hypothesis -

Alternative Hypothesis -

CPR (ae-23)

– We are going to take the proportion of “died”

– Calculate \(\hat{p_c} - \hat{p_t}\)

– Check assumptions

– Test our hypothesis using theory based methods

– Make decisions and conclusions based on a p-value

One Categorical Case

– Can you read Martian?

ae-23

Can you read Martian

How well can humans distinguish one “Martian” letter from another? In today’s activity, we’ll find out. When shown the two Martian letters, kiki and bumba, vote on whether you think bumba is option 1 or option 2.

Which letter is bumba?

Go to the link to vote: https://app.sli.do/event/etoay5PwN5Mg5qiYg6BnDf

Martian Alphabet

We are recording how many students correctly identified bumba

And are interested in if students can read Martian based on these data

Now that we have data, we can…

– Calculate our sample statistic

– Simulate a null distribution

– Calculate a p-value

– Make decisions and conclusions

Martian Alphabet

– Sample Statistic

– Null Hypothesis

– Alternative Hypothesis