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Math Help - Statistics questions

  1. #1
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    Statistics questions

    So this is the problem set up:
    32% of americans are in favor of outlawing cigarettes.
    200 random americans were asked if they are in favor
    54 were in favor of outlawing cigarettes
    Overall question: At a = 0.05, is there sufficient evidence to conclude that less than 32% of Americans are in favor of outlawing cigarettes?

    I've got step I:
    Step I:
    H0 : u = .32
    Ha: u != .32

    I need help with the rest (I'm stuck and don't know where to go from here!):

    Step II: Standardized statistic and its value (this is all it says)

    Step III: Decision rule

    Step IV: Conclusion




    A couple more problems that I'm not sure how to do:

    2: Pulse rates of a random sample of 6 patients were recorded before and after given a certain drug:
    Patient Before After
    1 82 78
    2 81 80
    3 83 76
    4 80 81
    5 85 79
    6 81 75


    Let ud be the mean reduction in the pulse rates due to the drug and assume that the population of paired differences is normally distributed.

    a) Find a 95% confidence interval for ud.
    What I have so far:
    ud = 3.83
    n = 6


    I think once I get this far I can do the rest.


    Thanks for all your help!!!!
    Last edited by merzbow; April 30th 2008 at 03:38 PM.
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  2. #2
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    Quote Originally Posted by merzbow View Post
    So this is the problem set up:
    32% of americans are in favor of outlawing cigarettes.
    200 random americans were asked if they are in favor
    54 were in favor of outlawing cigarettes
    Overall question: At a = 0.05, is there sufficient evidence to conclude that less than 32% of Americans are in favor of outlawing cigarettes?

    I've got step I:
    Step I:
    H0 : u = .32
    Ha: u != .32 Mr F says: No. It's Ha: u < 0.32.

    I need help with the rest (I'm stuck and don't know where to go from here!):

    Step II: Standardized statistic and its value (this is all it says)

    Step III: Decision rule

    Step IV: Conclusion

    [snip]
    There's a number of apporaches. One approach would be to construct a confidence at the desired significance level. See reply #3 of this thread for an example: http://www.mathhelpforum.com/math-he...-homework.html

    Another approach is to calculate the p-value.

    p-value = \Pr(X \leq 54 | X ~ Binomial(n = 200, p = 0.32).

    Compare this value with your chosen level of significance.
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  3. #3
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    Quote Originally Posted by merzbow View Post
    [snip]
    2: Pulse rates of a random sample of 6 patients were recorded before and after given a certain drug:
    Patient Before After
    1 82 78
    2 81 80
    3 83 76
    4 80 81
    5 85 79
    6 81 75


    Let ud be the mean reduction in the pulse rates due to the drug and assume that the population of paired differences is normally distributed.

    a) Find a 95% confidence interval for ud.
    What I have so far:
    ud = 3.83
    n = 6


    I think once I get this far I can do the rest.


    Thanks for all your help!!!!
    Read this: Paired Differences & Differences of Proportions

    Or this: The Paired-T Confidence Interval
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