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Exercise

Compare with classical methods

Agresti and Coull's classical interval method is available in your workspace as classical_binom_ci() and takes the arguments y, n and the confidence level conf.level.

For our example where 16 out of 20 students are concerned about being overweight, you can compute a 90% classical interval:

classical_binom_ci(16, 20, .90)

To compare between Bayesian and classical methods, suppose we assign P a uniform density (i.e. a \(beta(1, 1)\) curve).

Now you can construct a 90% Bayesian probability interval for P and compare this interval with the Agresti-Coull interval.

Instructions
100 XP
  • Define the number of successes y and the sample size n.
  • Use the classical_binom_ci() function to find a 90% confidence interval for P.
  • Define the vector of prior beta shape parameters ab if we are assigning a uniform prior for P.
  • Find the vector beta shape parameters ab_new for the posterior curve.
  • Using the qbeta() function, construct a 90% Bayesian probability interval and compare with the classical interval you found in the second instruction.