STAT100B_HW2S

STAT100B_HW2S - STAT 100B: Homework 2 Solutions Denise Tsai...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: STAT 100B: Homework 2 Solutions Denise Tsai January 31, 2011 1. Suppose we flip a coin 100 times independently and we get 55 heads. (a) Test H0 : p = 1/2 vs H1 : p > 1/2, and calculate the p-value. Solution: Z= p − p0 ˆ p0 (1−p0 ) n = 55 − 0.5 100 0.5(1−0.5) 100 =1 The p-value: P (Z > 1) = 1 − P (Z ≤ 1) = 1 = 0.8413 = 0.1587 We do not reject the null hypothesis. Therefore, there is strong evidence to claim that the coin is fair. (b) Suppose the decision rule is to reject H0 if p > .6. What is the probability of type ˆ I error? If the true value of p is .7, then what is the probability of type II error? Solution: P (Type I error) = P (reject H0 | H0 is true) 1 = P (ˆ > 0.6 | p = ) p 2 0.6 − 0.5 = P Z > = P (Z > 2) = 0.0228 0.5(1−0.5) 100 P (Type II error) = P (accept H0 | H1 is true) = P (ˆ ≤ 0.6 | p = 0.7) p 0.6 − 0.7 = P Z ≤ = P (Z ≤ −2.182) = 0.0146 0.7(1−0.7) 100 1 ...
View Full Document

Ask a homework question - tutors are online