Daily 12 - Mar 02

Class Performance

Students: 98 | Mean: 3.81 | Median: 4 | SD: 0.42

Scores ranged from 2 to 4 out of 4 points.

Score Distribution

Performance by Question

Questions

Q1: CLT Explorer — Distribution, Mean, SD

The CLT explorer assumes a population distribution that is exponential with a mean of 30.3 and a SD of 30.3.

  • Incorrect mean value — Some students wrote 3.8 or 3.4 instead of 30.3, likely misreading the CLT explorer display.
  • Wrong distribution type — A few students wrote “normal” instead of “exponential.” The CLT explorer specifically uses an exponential distribution.
  • Mixing up mean and SD — For the exponential distribution, the mean and SD are both 30.3. Some students provided different values for each.

Q2: True SE vs. Estimated SE

The true standard error is 5.533 (or 5.53). The estimated standard error is sample dependent — any specific numeric estimate (e.g., 3.462, 5.61) is acceptable.

  • Only providing one SE value — Some students gave only the true SE without a separate estimated SE value. Both are required.
  • Providing formulas without numbers — Writing the SE formulas (σ/√n, s/√n) without computing the actual numeric values.
  • Incorrect true SE — Some wrote 6.53 instead of 5.533. The true SE = σ/√n = 30.3/√30 ≈ 5.533.

Q3: Interval Prediction Challenge Bounds

The lower bound is 22 (or ~21.6) and the upper bound is 38 (or ~38.4) for the interval capturing 95% of all sample means.

  • Incorrect lower bound — One student wrote 30 as the lower bound. The interval is centered at 30.3 and extends roughly ±1.96 SE in each direction.
  • Incorrect upper bound — One student wrote 68 as the upper bound, far too wide. The 95% interval is approximately [22, 38].
  • Reversed or mismatched bounds — Some students provided bounds that didn’t form a symmetric interval around the mean of 30.3.

Q4: Best Regression Approximation Type

Regression provides the best linear approximation to the conditional expectation function (CEF).

  • Writing “causal” — Several students wrote “causal.” Regression estimates associations; it does not inherently provide causal estimates without additional assumptions.
  • Other incorrect terms — Students wrote “descriptive,” “metric,” “residualized,” “predictive,” or “direct.” The key term is specifically linear.
  • Confusing with variable types — Some wrote “dependent variable” or “independent variable.” The question asks about the type of approximation, not the variables involved.

Key Takeaways

Strengths: Exponential distribution identified correctly | SE values computed accurately | Interval bounds well understood.

Review:

  • Regression provides a linear approximation to the CEF — not causal, descriptive, or predictive
  • True SE = σ/√n — make sure to compute the numeric value, not just write the formula
  • Read CLT explorer values carefully — the mean is 30.3, not 3.03 or 3.8