The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 900900 voters in the town

Question

The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 900900 voters in the town and found that 42B% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 388%. Find the value of the test statistic. Round your answer to two decimal places.

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Nho 3 years 2021-09-04T16:09:21+00:00 1 Answers 0 views 0

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    2021-09-04T16:10:41+00:00

    Answer:

    The value of the test statistic is 2.47.

    Step-by-step explanation:

    The test statistic is:

    t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

    In which X is the sample mean, \mu is the expected mean, \sigma is the standard deviation and n is the size of the sample.

    For a proportion p, we have that:

    s = \frac{\sigma}{\sqrt{n}} = \sqrt{\frac{p(1-p)}{n}}

    A political study took a sample of 900 voters in the town and found that 42% of the residents favored annexation.

    This means that X = 0.42, n = 900

    Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 38%

    This means that the expected is \mu = p = 0.38

    So

    s = \frac{\sigma}{\sqrt{n}} = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.38*0.62}{900}} = 0.0162

    Find the value of the test statistic

    t = \frac{X - \mu}{s}

    t = \frac{0.42 - 0.38}{0.0162}

    t = 2.47

    The value of the test statistic is 2.47.

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