In Exercise 32.10 we assumed that all 98 students in the class made their responses independently. The test was X ∼ Binomial(98, p)

H0 : p = 0.5 H1 : p , 0.5.

In this question we’ll consider the independence assumption underlying the test. Say whether each of the following statements is true or false, and give a brief explanation of each answer.

Hint: to guide your answers, try thinking what would happen to X in the most extreme case of nonindependence, where one student makes a 50-50 guess and all the

a. Even if p = 0.5 other students copy the same guess. , we can only say that X ∼ Binomial(98, 0.5)

if everyone makes independent responses.

b. If some students copy a friend’s guess, X would tend to have greater variability than a Binomial(98, 0.5) distribution.

c. It could still be true that p = 0.5 even if people don’t guess independently.

d. Non-independent guesses won’t affect the P-value.