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22 January, 04:36

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 556 babies were born, and 278 of them were girls.

Use the sample data to construct a 99 % confidence interval estimate of the percentage of girls born.

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  1. 22 January, 08:26
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    To solve this problem, we make use of the z statistic. The formula for the confidence interval can be calculated using the formula:

    Confidence Interval = p ± MOE

    where,

    p is the portion of girls = 278 / 556 = 0.5

    MOE is the margin of error

    We calculate the margin of error using the formula:

    MOE = z * sqrt[p (1 - p) / n]

    From the standard distribution tables, the value of z at 99% confidence is:

    z = 2.58

    Therefore the MOE is:

    MOE = 2.58 * sqrt[0.5 (0.5) / 556]

    MOE = 0.055

    Therefore the confidence interval is:

    Confidence Interval = 0.5 ± 0.055

    Confidence Interval = 0.445, 0.555

    0.445
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