Statistics · Module 7
Answers and explanations · Put a range around an estimate
Compare these references after your own attempt. You can read them at any time; they do not record a live model or vendor run.
Statistics · Module 7
Compare these references after your own attempt. You can read them at any time; they do not record a live model or vendor run.
7A. SE=4/√16=1 minute. Margin=2.131×1=2.131 minutes. Interval=[17.869,22.131] minutes, about [17.87,22.13]. State that this is an interval for the model population mean under independent normal observations with unknown variance, not for individual durations.
7B. Correct wording: “This 95% confidence-interval procedure covers the fixed mean in about 95% of repeated samples under its assumptions.” It does not assign a frequentist 95% probability to the fixed mean after observing this particular interval. It also does not describe the fraction of individuals within the bounds; that would involve the outcome distribution or a prediction/tolerance method.
7C. The 99% interval is wider because the procedure needs a larger allowance to achieve higher long-run coverage. Precision and coverage trade off for the same data. Neither interval automatically corrects selection bias, missingness bias, model misspecification or measurement error.