18.05 Lecture Notes - Lecture 8: Mit Opencourseware
Document Summary
Problem 1. (10 pts. ) (a) let x = number of heads. Since ha is one-sided the rejection region is one-sided. Since ha says that is small it predicts a small number of heads in 12 tosses. That is, we reject h0 on a small number of heads. So, rejection region = left tail of null distribution. c0. 95 = qbinom(0. 05, 12, 0. 5) - 1 = 2. Rejection region is 0 x 2. p = pbinom(3, 12, 0. 5) = 0. 072998. Binomial(12,15) null distribution and rejection region x 2. Erika concludes there is not enough evidence to reject the null hypothesis at the signi cance level 0. 05. (b) let n = number of tosses that were tails before the third that is heads. Probability model: choose two tosses in the rst n+2 for heads; the n + 3rd toss must be heads: n + 2 (1 )n 3 . p(n) = This is called the negative binomial distribution with parameters 3 and .
