MATH 1105 · Probability and Statistics: Sampling and Inference

Led by Jerzy Neyman Simulacrum

The sampling distribution, the central limit theorem, the t-distribution, and confidence intervals — taught by the statistician who invented the confidence interval.

1. Module 1

   Study Design and Sampling

   Led by Jerzy Neyman Simulacrum

   The question

   A survey of 10,000 online volunteers finds 78% support stricter gun control. "Overwhelming evidence." Identify every methodological problem — and describe the study design that would produce valid inference.

   Outcome

   The student can distinguish study types, identify sampling bias, and explain why randomness enables inference.

   Sub-units

   1. ○ 1.1 Study Design Critique Open this unit → ✓ ↻
   Begin the course → Print certificate of completion
2. Module 2

   The Sampling Distribution of the Sample Mean

   Led by Jerzy Neyman Simulacrum

   The question

   Population mean 72, SD 15, sample size 100. P(x̄ > 74) ≠ P(X > 74). Why — and what does the central limit theorem guarantee about the shape of the sampling distribution?

   Outcome

   The student can describe the SDSM, apply the CLT, and compute probabilities involving sample means.

   Sub-units

   1. ○ 2.1 SDSM Calculations Open this unit → ✓ ↻
   Open this module → Print certificate of completion
3. Module 3

   The Sampling Distribution of the Sample Proportion

   Led by Jerzy Neyman Simulacrum

   The question

   True proportion p = 0.40, sample of 200, p̂ = 0.51. How many standard errors from the true proportion? What does this suggest about the sample — and what conditions must hold for the normal approximation to apply?

   Outcome

   The student can describe the SDSP, verify conditions for inference, and compute probabilities.

   Sub-units

   1. ○ 3.1 Sample Proportion Problems Open this unit → ✓ ↻
   Open this module → Print certificate of completion
4. Module 4

   The t-Distribution and Confidence Intervals

   Led by Jerzy Neyman Simulacrum

   The question

   Mean 72, SD 10, n = 25. What is the 95% CI? The 99% CI? A student says "there is a 95% probability the true mean is in this interval." Is that correct?

   Outcome

   The student can construct and correctly interpret confidence intervals for means and proportions.

   Sub-units

   1. ○ 4.1 Confidence Interval Construction Open this unit → ✓ ↻
   Open this module → Print certificate of completion
5. Module 5

   Putting Inference Together

   Led by Jerzy Neyman Simulacrum

   The question

   A journalist reports: "Scientists are 95% sure the drug reduces blood pressure by between 2.3 and 8.1 mmHg." Is this correct? If not, what does 95% confidence actually mean?

   Outcome

   The student can explain the frequentist confidence interval correctly and identify common misinterpretations.

   Sub-units

   1. ○ 5.1 Final Essay: What a Confidence Interval Actually Means Open this unit → ✓ ↻
   Open this module → Print certificate of completion