Results 1 to 2 of 2

Math Help - Calculate power in Statistics

  1. #1
    Member
    Joined
    Oct 2007
    From
    Nevada
    Posts
    188

    Calculate power in Statistics

    A cigarette manufacteror claims that the mean nicotine content of its cigarettes is 15 mg with a standard deviation of 0.25 mg. A simple random sample of 45 cigarettes is tested to determine the mean nicotine content. Using the following information, answer the questions.

    Ho: population mean = 1.5
    Ha: population mean > 1.5

    Reject Ho when sample mean > 1.85

    A.) Calculate the power of the test against the alternative value, alternative population mean =1.95. Assume a normal distribution.

    I know power is 1 - a Type II error (failing to reject a false hypothesis). However, do not know how to go about solving this.

    B.) What is the probability that you would make a Type II error.
    Please explain.
    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 DINOCALC09 View Post
    A cigarette manufacteror claims that the mean nicotine content of its cigarettes is 15 mg Mr F says: Strong cigarettes .... You'd only need to smoke 1 a day I imagine. Much healthier than if the content was 1.5 mg, say .....

    with a standard deviation of 0.25 mg. A simple random sample of 45 cigarettes is tested to determine the mean nicotine content. Using the following information, answer the questions.

    Ho: population mean = 1.5
    Ha: population mean > 1.5

    Reject Ho when sample mean > 1.85

    A.) Calculate the power of the test against the alternative value, alternative population mean =1.95. Assume a normal distribution.

    I know power is 1 - a Type II error (failing to reject a false hypothesis). However, do not know how to go about solving this.

    B.) What is the probability that you would make a Type II error.
    Please explain.
    Power = Pr(Type I error) = \Pr(\text{Reject} H_0 \, | \, \mu = 1.95) = \Pr(\overline{X} > 1.85 \, | \, \mu = 1.95).


    Pr(Type II error) = \Pr(\text{Accept} H_0 \, | \, \mu = 1.95) = \Pr(\overline{X} < 1.85 \, | \, \mu = 1.95).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Z- statistics? and how to calculate
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: June 13th 2011, 01:31 PM
  2. Calculate power of negative decimal number
    Posted in the Algebra Forum
    Replies: 13
    Last Post: May 14th 2011, 10:22 AM
  3. Calculate output power based on speed
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: December 31st 2009, 09:55 AM
  4. Statistics : to calculate mean and variance
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 3rd 2008, 09:07 PM
  5. calculate power
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: December 12th 2007, 09:30 AM

Search Tags


/mathhelpforum @mathhelpforum