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24 March, 14:21

In a random sample of 200 Americans, 51% said they favor building more nuclear power plants. In a random sample of 150 French, 48% said they favor building more nuclear power plants. At? = 0.10, is there enough evidence to say the proportions are the same?

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  1. 24 March, 15:58
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    Yes, there is enough evidence to say the proportions are the same.

    Step-by-step explanation:

    Null hypothesis: The proportions are the same.

    Alternate hypothesis: The proportions are not the same.

    Data given:

    p1 = 51% = 0.51

    n1 = 200

    p2 = 48% = 0.48

    n2 = 150

    pooled proportion (p) = (n1p1 + n2p2) : (n1 + n2) = (200*0.51 + 150*0.48) : (200 + 150) = 174 : 350 = 0.497

    Test statistic (z) = (p1 - p2) : sqrt[p (1-p) (1/n1 + 1/n2) = (0.51 - 0.48) : sqrt[0.497 (1-0.497) (1/200 + 1/150) ] = 0.03 : 0.054 = 0.556

    The test is a two-tailed test. At 0.10 significance level the critical values - 1.645 and 1.645

    Conclusion:

    Fail to reject the null hypothesis because the test statistic 0.556 falls within the region bounded by the critical values.
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