﻿ Review of Distributions in Advanced Statistics I

# HAP 719: Advanced Statistics I

## Lecture

• Read Chapter 4, Distributions in Big Data in Healthcare: Statistical Analysis of the Electronic Health Records, Health Administration Press, 2020.
• Read Chapter 6, pages 135-152 in Big Data in Healthcare: Statistical Analysis of the Electronic Health Records, Health Administration Press, 2020.
• Yili Lin's Lecture Slides►
• Normal distribution  Slides► Video►  YouTube►
• Yoita's review of Normal distribution Video►
• Yoita's review of hypothesis testing Video►
• Visual probability calculator for a variety of distributions More►
• Probability distributions & expectations Slides►  Video► YouTube►
• Average of everything becomes Normal. The following are non-Normal distributions that are being sampled.  As the sample size increases, the distribution of the average becomes more Normal.

## Assignments

Assignments are submitted on blackboard.  They are graded as pass/fail.  A summary 1-page word document should be included.  In the summary, you should state if you were able to get the same answers as those provided. Your R, STATA, or Python code should be included in separate files. No late assignments are accepted.  It is OK to help each other in doing the assignments but not OK to copy and paste work of others.  It is OK to use ChatGPT or other large language models to generate the R code, but you must be transparent about it and report its use.

Question 1: A particular health related test  has a mean score of 500 and a standard deviation of 100.  In a sample of 30 students the mean test score was 525 and standard deviation was 75.  (a) Test that the sample comes from the population.  (b) draw the two distributions. (c)  Provide a confidence interval for the mean of the sample.

Resources for Question 1:

• Answer on page 147 to 150 in the required textbook
• Yili Lin's Answer► R Code►
• Sai Naga Akshar Gollapudi, Bessy Nicole Lovos Davila, and Maria Kurian Teach One►

Question 2: Assume that the average length of stay for individuals having cardiac by-pass surgery is normally distributed with a mean of 9 days and a standard deviation of 1.25 days.  What is the probability that a random by-pass patient will have length of stay of 8 days.

Resources for Question 2:

Question 3: Calculate the probability of the following events for a distribution with mean 10 and standard deviation 5.

1. P(X≤12)
2. P(X≥22)
3. P(2≤X≤12)

Resources for Question 3: