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Null hypothesis question

  1. Feb 18, 2013 #1
    1. The problem statement, all variables and given/known data

    A manufacturing company produces water filters for home refrigerators. The process has typically produced about 4% defective. A recently designed experiment has led to changing the seal to reduce defects. With the process running using the new seal, a random sample of 300 filters yielded 7 defects.

    2. Relevant equations

    H0: null hypothesis
    H1: alternative hypothesis

    3. The attempt at a solution

    H0: p not equal to 7/300?
    H1: p=7/300?

    I have looked up examples of null hypothesis but I am not sure how to apply it to this problem.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 18, 2013 #2

    Mark44

    Staff: Mentor

    The null hypothesis should involve the population statistic, not the observed sample statistic.

    So your null hypothesis should be H0: p = .04

    Can you infer from the problem statement what the alternate hypothesis should be?
     
  4. Feb 18, 2013 #3
    would it be H1: p ≠ .04?
     
  5. Feb 18, 2013 #4

    Mark44

    Staff: Mentor

    No.
    What does this suggest to you?
     
  6. Feb 18, 2013 #5
    H1: p < .04?
     
  7. Feb 18, 2013 #6

    Mark44

    Staff: Mentor

    Yes. In ordinary language, the null hypothesis is: The new seal makes no difference. The alternate hypothesis is: The new seal reduces the defect rate.
     
  8. Feb 18, 2013 #7
    Okay, I got that the test statistic is -1.5 by doing Z=(.023-.04)/sqrt(.04*.96/300) is this correct? And how would I find the critical value at a .05 level of significance? By the way thank you so much for all the help.
     
  9. Feb 18, 2013 #8

    Mark44

    Staff: Mentor

    What you got looks OK to me.

    To find the critical value, look in a table of the standard normal distribution for the number in the table that is closest to 0.9500, and read off the z value for that probability. What this is telling you is P(Z < something) = .9500. That "something" will be a positive value. What you want for your critical value is -<something>, the value such that P(Z < -(something)) = .0500.

    It helps to draw a sketch of the standard normal (Z) distribution, and recognize that it has symmetry across the vertical axis.
     
  10. Feb 18, 2013 #9
    Okay my table has Z.005=1.645 so I would use -1.645 for my critical value I believe? and the final part of this question which I am unsure about it is I need the p value which I know is the probability of getting the sample results.
     
  11. Feb 18, 2013 #10

    Mark44

    Staff: Mentor

    Before, you said at the .05 level. Is the above a typo or did you look at the wrong value?
     
  12. Feb 18, 2013 #11
    yes sorry I meant .05 not .005
     
  13. Feb 18, 2013 #12

    Mark44

    Staff: Mentor

    I corrected the .005 that you had.
    Yes.
    So if Z < -1.645, you would accept the alternate hypothesis.

    In your earlier calculation, you got Z = -1.5.
     
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