Statistical inference

Concepts

• Random sample 10 exercisesA random sample of size n is a set of n independent random variables X_i, all with the same distribution, that represent n observ…
• Sample mean 10 exercisesThe sample mean bar X is the arithmetic average of the n variables X_i of a random sample; since it depends on the sample, it is…
• Estimator 10 exercisesAn estimator hatθ is a rule T, a function of the random sample X_i, that produces a value used to approximate an unknown populati…
• Confidence interval 10 exercisesA confidence interval [L,U] is a range of values, computed from the sample X, that contains the parameter θ with a preset probabi…
• Hypothesis test 10 exercisesA hypothesis test is a rule that, from sample data, decides whether to reject the null hypothesis H_0, which fixes a value θ_0 fo…
• p-value 10 exercisesThe p-value is the probability P, computed assuming the null hypothesis H_0 is true, of obtaining a result at least as extreme as…