Assessment :Inferential Statistical Analysis with Python (Statistics with Python Specialization) Answers 2025

1) Question 1 — 95% CI for the undergraduate mean (n=500, mean=62.5, SD=10)

SE = 10 / √500 ≈ 0.4472; margin = 1.96·SE ≈ 0.8765 ⇒ CI ≈ (62.5 ± 0.8765) = (61.6235, 63.3765)

❌ (62.46, 62.54)
✅ (61.62, 63.38)
❌ (42.90, 82.10)
❌ (62.05, 62.95)

Explanation: Using z≈1.96 for 95% (n large), the CI is 62.5 ± 1.96·(10/√500) ≈ (61.62, 63.38).

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2) Question 2 — Conclusion about hypothesized mean of 63 (given the CI above)

❌ We have evidence against this hypothesized mean.
✅ We have evidence in support of this hypothesized mean.

Explanation: 63 lies inside the 95% CI (61.62, 63.38), so the data do not contradict 63; we would fail to reject H₀ that μ = 63 at α = 0.05.

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3) Question 3 — How to interpret the CI from Problem 1

❌ There is a 95% chance that the true undergraduate mean lies in this interval.
❌ 5% of all potential values for the true mean lie outside of this interval.
❌ The p-value for testing a null hypothesis that the mean is 63 is 0.05.
✅ 95% of all confidence intervals computed this way will cover the true population mean (in expectation).

Explanation: Correct frequentist interpretation: over many repeated samples, 95% of CIs constructed the same way will contain the true mean.

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4) Question 4 — Decision about H₀ given t = -1.12, df = 499, p = 0.264, α = 0.05

❌ We reject it; the mean is significantly lower than this hypothesized mean.
❌ We reject it; the mean is significantly different from this hypothesized mean.
✅ We fail to reject it; the mean is not significantly different from this hypothesized mean.
❌ We do not have enough information to make a decision.

Explanation: p = 0.264 > 0.05, so we do not reject H₀. No significant evidence that the mean differs from 63.

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5) Question 5 — Conclusion from 95% CI for difference in proportions = (−0.05, 0.09)

❌ The sample sizes are too small to make any meaningful inference about the difference in proportions.
✅ There is no evidence at all of the experimental pill being effective; the proportions are statistically identical.
❌ The experimental pill produced a significant improvement in the proportion experiencing pain relief within one hour.
❌ We need to know the proportions to make a decision.

Explanation: The 95% CI for (treatment − control) contains 0, so we cannot conclude a nonzero difference; there is no statistical evidence of effectiveness at the 5% level.

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🧾 Summary Table

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