Results 1 to 3 of 3

Math Help - Probability of Type I and II errors when P = a number

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    4

    Probability of Type I and II errors when P = a number

    I have the following problem:
    "When a thread-cutting machine is operating properly, only 2% of the units produced are defective. Since the machine was bumped by a forklift, the quality-control manager is concerned that it may require expensive downtime and readjustment. The manager wishes to test, null hypothesis H0: P =< 0.02 against H1: P > 0.02. Using a random sample of 400 units, his decision rule for the test is defined as: Reject H0 if P-hat > 0.034; and don't reject H0 if P-hat =< 0.034."
    a) Find probability of Type I error (alpha) when P = 0.02
    b) Find probability of Type II error (beta) and the power, when P = 0.04
    c) Find power of test when the true proportion P = 0.05

    My issue is, we just started this material (what H0 and H1 is, and the two types of errors) and have not covered this yet. So, I went to the book to gain a clue. I assume since P is =< 0.02, we will want to use a right tail/upper tail test. However, I'm not sure if we use Z or t, and really, where I go from here to answer a b and c.

    Please help?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by oxyron View Post
    I have the following problem:
    "When a thread-cutting machine is operating properly, only 2% of the units produced are defective. Since the machine was bumped by a forklift, the quality-control manager is concerned that it may require expensive downtime and readjustment. The manager wishes to test, null hypothesis H0: P =< 0.02 against H1: P > 0.02. Using a random sample of 400 units, his decision rule for the test is defined as: Reject H0 if P-hat > 0.034; and don't reject H0 if P-hat =< 0.034."
    a) Find probability of Type I error (alpha) when P = 0.02
    b) Find probability of Type II error (beta) and the power, when P = 0.04
    c) Find power of test when the true proportion P = 0.05

    My issue is, we just started this material (what H0 and H1 is, and the two types of errors) and have not covered this yet. Mr F says: Then wouldn't it be better then to wait until it has been covered ....?

    So, I went to the book to gain a clue. I assume since P is =< 0.02, we will want to use a right tail/upper tail test. However, I'm not sure if we use Z or t, and really, where I go from here to answer a b and c.

    Please help?
    (0.034)(400) = 13.6.

    a) Calculate Pr(X > 13 | X ~ Binomial(p = 0.02, n = 400)).

    b) Calculate Pr(X < 14 | X ~ Binomial(p = 0.04, n = 400)).

    Power = 1 - \beta.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    4
    Mr F says: Then wouldn't it be better then to wait until it has been covered ....?
    I agree 100% with you. However the professor gave it out on Tuesday and it is due today (Thursday), so I don't have much choice in what we cover or when it needs to be turned in. Thanks for the assistance, by the way.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Type 1 and Type 2 Errors
    Posted in the Statistics Forum
    Replies: 1
    Last Post: May 31st 2011, 08:51 AM
  2. type I and II errors
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: February 18th 2010, 11:37 PM
  3. Super stuck on Type 1 and Type 2 errors
    Posted in the Statistics Forum
    Replies: 0
    Last Post: January 29th 2010, 12:06 PM
  4. Type I and Type II errors with sigma given...
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: January 20th 2010, 03:09 PM
  5. Probability of type I and II errors!!!!!!!!
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: October 16th 2008, 03:15 AM

Search Tags


/mathhelpforum @mathhelpforum