Duality Between Confidence Intervals and Hypothesis Testing (Lecture Notes for Lecture 7)

1. Use a two-sided confidence level \(c\) confidence interval to perform a two-sided significance level \(\alpha\) hypothesis test.
2. Explain, loosely, why we reject a point (two-sided) null hypothesis when the null value of the parameter does not fall in a confidence interval.
3. Compare and contrast accept/reject hypothesis testing with confidence intervals in terms of their strengths and weaknesses.

Practical versus Statistical Significance (Lecture Notes for Lecture 7)

1. Explain the difference between statistical and practical significance.
2. Give the origin of the phrase “statistical significance.”
3. Explain why a \(P\)-value, on its own, indicates nothing about practical significance.
4. Explain how a confidence interval can be used to identify both statistical and practical significance.
5. Construct a hypothetical scenario where a result may be:
   • statistically significant but not practically significant.
   • practically significant but not statistically significant.

Confidence Curves (Lecture Notes for Lecture 7)

1. Give a constructive definition of a confidence curve in terms of two-sided confidence intervals for a population parameter.
2. State how to construct the confidence curve for the mean of a Gaussian population.
3. State how to construct the confidence curves for the population slope and intercept under the SLRGN model.
4. Given a confidence curve for a population parameter and a ruler, identify:
   • a point estimate for a population parameter
   • a confidence level \(c\) confidence interval for the population parameter
   • a \(P\)-value for the two-sided hypothesis test for the point null hypothesis \(\theta = \theta_{0}\).
5. Interpret a confidence curve in terms of what it indicates about our certainty about the value of a population parameter.

confcurve in R (Lecture Notes for Lecture 7)

1. Use confcurve to plot SLRGN confidence curves for the population slope and intercept using an output from lm.
2. Use confcurve to compute SLRGN two-sided \(P\)-values for the population slope and intercept using an output from lm.