An Introduction to Probability and Statistical Inference, 2nd Edition

Exercises

3.1

(i) In reference to Example 8 in Chapter 1, the appropriate model is the Binomial model with X_i = 1 if the ith young adult listens to the program, and X_i = 0 otherwise, where P(X_i = 1) = p, and the X_i's are independent, so that $X={\displaystyle {\sum }_{i=1}^n{X}_i\sim B\left(n,p\right)}$.

(ii) The claim is that p > p₀ some specified number 0 < p₀ < 1, and the claim is checked by testing the hypothesis H₀: p ≤ p₀ against the alternative H_A: p > p₀ at level of significance α.

(iii) For p₀ = 5%, n = 100, and α = 0.02, use the CLT to carry out the test.

3.2

(i) In reference to Example 9 in Chapter 1, the appropriate model is the Binomial model with X_i = 1 if the ith item is ...