Big babies: The National Health Statistics Reports described a study in which a sample of 315 one-year-old baby boys were weighed. Their mea

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Big babies: The National Health Statistics Reports described a study in which a sample of 315 one-year-old baby boys were weighed. Their mean weight was 25.6 pounds with standard deviation 5.3 pounds. A pediatrician claims that the mean weight of one-year-old boys is greater than 25 pounds. Do the data provide convincing evidence that the pediatrician’s claim is true? Use the =α0.05 level of significance and the critical value method with the

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Xavia 5 months 2021-08-18T17:16:48+00:00 1 Answers 12 views 0

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    2021-08-18T17:18:39+00:00

    Answer:

    The pvalue of the test is 0.0012 < 0.05, which means that the data provides convincing evidence that the pediatrician’s claim is true.

    Step-by-step explanation:

    A pediatrician claims that the mean weight of one-year-old boys is greater than 25 pounds.

    This means that at the null hypothesis, we test that the mean is 25 pounds, that is:

    H_0: \mu = 25

    At the alternate hypothesis, we test that it is more than 25 pounds, that is:

    H_a: \mu > 25

    The test statistic is:

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

    In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

    25 is tested at the null hypothesis:

    This means that \mu = 25

    The National Health Statistics Reports described a study in which a sample of 315 one-year-old baby boys were weighed. Their mean weight was 25.6 pounds with standard deviation 5.3 pounds.

    This means that n = 315, \mu = 25.6, \sigma = 5.3

    Value of the test-statistic:

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

    z = \frac{25.6 - 25}{\frac{5.3}{\sqrt{315}}}

    z = 3.04

    Pvalue of the test and decision:

    The pvalue of the test is the probability of finding a mean above 25.6 pounds, which is 1 subtracred by the pvalue of z = 3.04.

    Looking at the z-table, z = 3.04 has a pvalue of 0.9988

    1 – 0.9988 = 0.0012

    The pvalue of the test is 0.0012 < 0.05, which means that the data provides convincing evidence that the pediatrician’s claim is true.

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