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    Confidence Interval

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    Please provide step by step instructions using actual numbers instead of formulas for solving the following 3 problems, thanks

    3. Determine whether the average number of calories in a homemade cookie is more than a store-bought one. Estimate the difference in the mean calories between the two types using a 90% confidence interval.
    homemade n=40 x-bar=180 s=2
    storebought n=45 x-bar=179 s=4

    4. A childcare agency was interestin in examining the amount that families pay per child per month for childcare outside the home. A randome sample of 64 families was selected and the mean and the standard deviation were computed to be $675 and $80 respectively.
    a. Find a 95% confidence interval for the true average amount spent per child per month for childcare outside the home.
    b. Interpret the interval found in part a.
    c. A social worker claims that the average amount spent per child per month outside the home is $700. Based on the interval in part a can this claim be rejected?
    d. Find a 95% upper confidence bound for the true average amount spent per child per month on childcare outside the home.

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    Solution Preview

    3. Solution. Xbar=180, sx=2,n1=40, Ybar=179, sy=4, n2=45, 1-alpha=0.1, so a=alpha/2=0.05
    t_0.05(n1+n2-2)=1.658.
    therefore, we get the confidence interval of the difference in the mean of two types as ...

    Solution Summary

    The expert determines whether the average number of calories in a homemade cookie is more than a store-bought one. The difference in the mean calories between the two types using a 90% confidence interval is estimated.

    $2.49

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