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Math Help - Hypothesis testing!

  1. #1
    Member javax's Avatar
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    Hypothesis testing!

    Hello everyone!

    A TV producer claims that 40 percent of parents watch his TV show. By the time when the show was transmitted, 100 parents were called on the phone, and it was found that 30 of them were watching the show. With \alpha = 0.05, was the producer right?

    I'm confused with the standard deviation here! There isn't and I don't know how to find it!


    THanks
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    Quote Originally Posted by javax View Post
    Hello everyone!

    A TV producer claims that 40 percent of parents watch his TV show. By the time when the show was transmitted, 100 parents were called on the phone, and it was found that 30 of them were watching the show. With \alpha = 0.05, was the producer right?

    I'm confused with the standard deviation here! There isn't and I don't know how to find it!


    THanks
    p denotes the probability of parents watching the show.

    Set the hypothesis using one-tailed test for the significance level of 0.05 as follows:

    H_0: p=0.4 for the TV producer's claim is correct.
    H_1: p < 0.4 for the claim is false.

    If z_c < z_{0.05} we can reject the hypothesis.

    \mu = NP = 100 (0.4)=40 and \sigma = \sqrt{Npq}=\sqrt{(100)(0.4)(0.6)}=4.90

    z_c = \frac{30-40}{4.90}=-2.04 < z_{0.05}

    Based on the samples, using one-tailed test, we can reject the hypothesis at significance level of 0.02. The evidence indicates almost overwhelmingly that the TV producer's claim is false.
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