Results 1 to 4 of 4

Thread: 2-sided alternative hypothesis

  1. #1
    Newbie
    Joined
    Jun 2009
    Posts
    10

    2-sided alternative hypothesis

    Assuming the rest of my work is correct for this question, I am having trouble on part c. I don't know if I have the right formula and, if I do, I don't know how to calculate $\displaystyle t_{\frac{0.025}{2}}$.

    Let X equal the length of wood blocks manufactured. Assume distribution of X is $\displaystyle N(\mu,\sigma^{2})$. The greatest lenth is 7.5 inches. We shall test the null hypothesis $\displaystyle H_{0}: \mu=7.5$against a 2-sided alternative hypothesis using 10 observations.

    a) Define test statistic and critical region for an$\displaystyle \alpha=0.05$ significance level.

    test statistic- $\displaystyle t=\frac{\bar{x}-7.5}{\frac{s}{\sqrt{10}}}$

    critical region- $\displaystyle |t|=\frac{|\bar{x}-7.5|}{\frac{s}{\sqrt{10}}} \ge t_{\frac{\alpha}{2}}(10-1)=2.262$

    Calculate the value of the test statistic and give your decision using the following data (n=10)
    7.65
    7.60
    7.65
    7.70
    7.55
    7.55
    7.40
    7.40
    7.50
    7.50

    $\displaystyle \bar{x}=\frac{75.5}{10}=7.55$
    $\displaystyle s^{2}=0.01056$
    s=0.10274

    t=1.539
    1.539 is not greater than 2.262, therefore, it fails to reject $\displaystyle H_{0}: \mu=7.5$

    c) Is $\displaystyle \mu=7.50$ contained in a 95% confidence interval for $\displaystyle \mu$?

    $\displaystyle \bar{x}+/- t_{\frac{0.025}{2}}(n-1)(\frac{s}{\sqrt{n}})$

    As of now, I am using my values of $\displaystyle \bar{x}=7.55$, s=0.10274 and n=10

    Thank you for helping!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    You would only need to know $\displaystyle t_{0.025/2} $ if you were calculating a 97.5% confidence interval for $\displaystyle \mu $ .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2009
    Posts
    10
    I didn't understand that either. My book seems to use that for the two sided hypotheses when finding the confidence interval. Is there a different formula I should use? or the same without dividing $\displaystyle \alpha$ by 2.

    The critical region equation for hypotheses one mean and variance unknown written in the book for H1: $\displaystyle \mu$ does not equal $\displaystyle \mu_{0}$ is $\displaystyle |\bar{x}-\mu_{0}| \ge t_{\frac{\alpha}{2}}(n-1)\frac{s}{\sqrt{n}}$
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    Quote Originally Posted by larz View Post
    I didn't understand that either. My book seems to use that for the two sided hypotheses when finding the confidence interval. Is there a different formula I should use? or the same without dividing $\displaystyle \alpha$ by 2.

    The critical region equation for hypotheses one mean and variance unknown written in the book for H1: $\displaystyle \mu$ does not equal $\displaystyle \mu_{0}$ is $\displaystyle |\bar{x}-\mu_{0}| \ge t_{\frac{\alpha}{2}}(n-1)\frac{s}{\sqrt{n}}$
    $\displaystyle \alpha = 0.05 $ in your problem
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Null Hypothesis, Alternative hypothesis, Critical Region..
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: Aug 8th 2011, 10:46 PM
  2. Alternative to (x+dx)^-2
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Jan 31st 2010, 11:45 AM
  3. Determining a null and alternative hypothesis
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: Dec 7th 2009, 07:47 AM
  4. any alternative method
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Jul 11th 2009, 03:35 AM

Search Tags


/mathhelpforum @mathhelpforum