A confidence interval for the usable-sample rate
Work through the usable-kit proportion, its standard error, the 95% confidence interval, and a careful interpretation. The walkthrough ends after part (a).
Johns Hopkins University · Fall 2026 · EN.553.211
Probability & Statistics
for the Life Sciences
A place to revisit class. Read the notes, follow an idea through the slides, and check your understanding.
Zan Ahmad Sections 05 & 06
This week: Hypothesis testing ↓October 28, 2026
Recorded lectures
Watch, pause, and work along
Hypotheses, p-values, and significance
Build a null reference model, calculate one- and two-sided p-values, and use the GPA example to make a significance decision.
Open or download MP4
Covered through original slide 20, “Significance level,” including the qualitative p-value evidence bands. We resume at slide 21, “Significance level & critical values.”
Follow the course
Notes & animated lectures
In class order · earliest to latest
Covariance, correlation & regression
See how two quantities move together, then build a line that describes their relationship.
Foundations of probability & counting
Start with outcomes and events. Build probability rules, permutations, combinations, and careful counting.
Conditional probability, independence & Bayes
Change the reference group, follow probability paths, and use evidence to update a probability.
Random variables, expectation & variance
Turn outcomes into numbers. Connect probability masses to averages, spread, transformations, and sums.
Counting models
One Bernoulli trial leads to binomial, hypergeometric, and Poisson counts. Compare assumptions, probabilities, means, and variances.
Formula and concept review
Connect data summaries, probability, conditioning, and discrete models with course notation, formulas, and click-controlled diagrams.
Continuous random variables & the normal distribution
Move from probability mass to density and area. Explore cumulative probability, uniform and normal distributions, standardization, and percentiles.
Confidence intervals
Build confidence intervals for means and proportions, interpret confidence and precision, and plan sample sizes. Follow the notes in class order and try three practice problems.
Hypothesis testing
Connect hypotheses, null distributions, p-values, and significance. Friday practice links these ideas to Chapter 7 confidence intervals. Questions begin on page 4; the final page is an optional continuation.
Slides pause at each step. Use the arrow keys or on-screen controls; a laptop or tablet works best for the animations.
Another way to see it
Selected 3Blue1Brown videos
Optional visual companions
Bayes theorem, the geometry of changing beliefs
An area picture for changing the reference group and updating beliefs.
3Blue1Brown · YouTubeThe medical test paradox, and redesigning Bayes’ rule
A diagnostic-testing example that makes the role of the base rate visible.
3Blue1Brown · YouTubeBinomial distributions | Probabilities of probabilities, part 1
A visual companion to repeated trials and binomial counts. The later inference material is optional.
3Blue1Brown · YouTubeThe quick proof of Bayes’ theorem
A short Bayes proof with a discussion of independence.
3Blue1Brown · YouTubeBut what is the Central Limit Theorem?
Further intuition for the normal distribution and the Central Limit Theorem. You do not need to know the binomial-to-normal approximation formulas.
3Blue1Brown · YouTubeThe final video includes a discussion of independence alongside the Bayes proof.