1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Statistics: What is the probability of type I error?

  1. Mar 5, 2014 #1
    1. The problem statement, all variables and given/known data

    X is a random variable of binomial distribution of parameter n=10 and unknown parameter p. Hypotheses are given as follows:

    [itex] H_0 \;\; : \;\; p=0.6 [/itex]

    [itex] H_1 \;\; : \;\; p \neq 0.6 [/itex]

    Suppose rejection region for [itex] H_0 [/itex] is [itex] \{X \leq 1\} \cup \{X \geq 9\} [/itex]

    Question 1: What is the probability of type I error?

    Question 2: If [itex] H_1 [/itex] is changed to "[itex] H_1 \;\; : \;\; p =0.3 [/itex]", then what is the probability of type II error?

    2. Relevant equations

    Binomial Distribution of parameters n and p: [itex] f(x) = \binom{n}x p^x(1-p)^{n-x} [/itex]

    3. The attempt at a solution

    Answer 1: Desired probability is

    [itex] P(X \leq 1,\;\; X \geq 9|p=0.6)=1-P(2\leq X \leq 8|p=0.6)= 1-\sum_{k=2}^8 \binom{10}k 0.6^k(1-0.6)^{10-k} \approx 0.1689 [/itex]

    Answer 2:

    [itex] P(2 \leq X \leq 8|p=0.3) = \sum_{k=2}^8 \binom{10}k 0.3^k(1-0.3)^{10-k} \approx 0.617 [/itex]

    Are these answers correct? Thank you in advance!
    Last edited: Mar 5, 2014
  2. jcsd
  3. Mar 29, 2014 #2

    Does anyone know the correct solution?
  4. Mar 30, 2014 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    I get 0.04803512320 ≈ 0.0480 for question 1 and .8505479682 ≈ 0.8585 for question 2.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted