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Math Help - Difficult Single Sample Hypotheses Test

  1. #1
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    Difficult Single Sample Hypotheses Test

    It is believed that 1.333% of all the TV's manufactured by a company are defective. Suppose that a random sample of 800 new TV's manufactured by this company has 16 defectives.

    Test, at 5% significance level, to see if the data provide enough evidence to conclude that the true defective rate is different from 1.333%. Don't forget to state the null and the alternative hypotheses.

    Also, what type of error might you have made in reaching your decision? Finally, compute the p-value for your test and use this p-value to decide if
    H0 can be rejected when alpha=0.2 (instead of 0.05).



    I've made several attempts and could not figured it out. Is there anyone who can show me how to do this question?

    Thanks.

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  2. #2
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    See AP Statistics Tutorial: Hypothesis Test for a Proportion

    If you reject then you are risking a type I error, while if you fail to reject you are risking a type II error.
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  3. #3
    MHF Contributor matheagle's Avatar
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    Most likely, they are using the central Limit Theorem here, on this binomial distribution.
    BUt with p near zero, the Poisson may be more appropriate.

    =.01333" alt="H_o=.01333" /> vs. \ne .01333" alt="H_a\ne .01333" />

    test stat is Z^*={\hat p-p_o\over \sqrt{p_oq_o/n}}

    where \hat p={16\over 800}

    p-value is 2P(Z>|Z^*|)
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