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25 May, 09:04

The U. S. Department of Agriculture claims that the mean cost of raising a child from birth to age 2 by husband-wife families in the United States is $13,120. A random sample of 500 children (age 2) has a mean cost of $12,925 with a standard deviation of $1745. At α=.10, is there enough evidence to reject the claim? (Adapted from U. S. Department of Agriculture Center for Nutrition Policy and Promotion).

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  1. 25 May, 09:06
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    Step-by-step explanation:

    We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

    For the null hypothesis,

    µ = 13120

    For the alternative hypothesis,

    µ ≠ 13120

    This is a 2 tailed test

    Since the population standard deviation is not given, the t test would be used to determine the test statistic. The formula is

    t = (x - µ) / (s/√n)

    Where

    s = sample standard deviation

    x = sample mean

    µ = population mean

    n = number of samples

    From the information given,

    µ = $13120

    x = $12925

    n = 500

    s = $1745

    t = (12925 - 13120) / (1745/√500) = - 2.5

    Degree of freedom = n - 1 = 500 - 1 = 499

    Using the t score calculator to find the probability value,

    p = 0.012

    Since α = 0.10 > p = 0.012, it means that there is enough evidence to reject the claim
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