Explore BrainMass
Share

Explore BrainMass

    Normal distribution to approximate binomial distribution

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Decide whether the normal distribution can be used to approximate the binomial distribution. If it can, use the z-test to test the claim about the population proportion p for the given sample statistics and level of significance a.
    ^
    A. Claim: p < 0.70; a = 0.01 Statistics: p = 0.50, n = 68
    ^
    B. Claim: p < 0.50; a = 0.10 Statistics: p = 0.71, n = 129

    Test the claim about the indicated population parameter with ? a (X^2) -test using the given sample statistics and level of significance a. Assume the population is normally distributed.

    A. Claim: ? ^2 ? 60 a = 0.025
    Statistics: s?2 = 72.7, n = 15

    B. Claim: ? ? 0.035: a = 0.01
    Statistics: s = 0.026, n = 16

    I have worked these several times but can't seem to get the answer. Thanks

    © BrainMass Inc. brainmass.com October 10, 2019, 6:06 am ad1c9bdddf
    https://brainmass.com/statistics/probability/normal-distribution-approximate-binomial-distribution-529372

    Solution Preview

    Hi there,

    Thanks for letting me work on your post. Here is my explanation:

    A. since np=68*0.50=34>5, nq=68*0.5=34>5, we could use the normal distribution can be used to approximate the binomial distribution.
    Null hypothesis: p>=0.70
    Alternative hypothesis: p<0.70
    At 0.01 significance level, the critical z value is -2.326
    test value ...

    Solution Summary

    The normal distribution to approximate binomial distributions are examined.

    $2.19