A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 300 babies were​ born, and 270 of th

Question

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 300 babies were​ born, and 270 of them were girls. Use the sample data to construct a 99​% confidence interval estimate of the percentage of girls born. Based on the​ result, does the method appear to be​ effective?

in progress 0
Nevaeh 2 weeks 2021-10-13T05:52:22+00:00 1 Answer 0

Answers ( )

    0
    2021-10-13T05:53:23+00:00

    Answer:

    99% confidence interval would be given (0.98;1).

    We are confident that about 98% to 100% of the babies born using this new method will be girls.  So is very effective since increase the probability of getting a girl by almost the double.

    Step-by-step explanation:

    1) Data given and notation  

    n=300 represent the random sample taken    

    X=270 represent the number of girls born in the sample selected

    \hat p=\frac{270}{300}=0.9 estimated proportion of girls born with the new method

    Confidence =99% or 0.99

    p= population proportion of girls born with the new method proposed

    2) Confidence interval

    The confidence interval would be given by this formula

    \hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

    For the 99% confidence interval the value of \alpha=1-0.99=0.01 and \alpha/2=0.005, with that value we can find the quantile required for the interval in the normal standard distribution.

    z_{\alpha/2}=2.58

    And replacing into the confidence interval formula we got:

    0.99 - 2.58 \sqrt{\frac{0.99(1-0.99)}{300}}=0.98

    0.99 + 2.58 \sqrt{\frac{0.99(1-0.99)}{300}}=1.00

    And the 99% confidence interval would be given (0.98;1.00).

    We are confident that about 98% to 100% of the babies born using this new method will be girls.  So is very effective since increase the probability of getting a girl by almost the double.

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )