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Rates of infant mortality, birth defect, and premature labor are high for babies with low birth...

Rates of infant mortality, birth defect, and premature labor are high for babies with low birth weight. There are many factors that may contribute to low birth weight.

In this activity, we use data from a random sample of women who participated in a study in 1986

For the 30 women in the study with a history of premature labor, a proportion of 18/30 = 0.60 (60%) had babies with low birth weight. For the remaining 159 women, a proportion of 41/159 = 0.26 (26%) had babies with low birth weight.

We now investigate the following research question: do the data provide evidence that the proportion of babies born with low birth weight is higher for women with a history of premature labor? This question is answered with a hypothesis test. To conduct the test we use a 1% level of significance.

State the test statistic and P-value. Interpret these values. Give a conclusion in context, and discuss whether a causal conclusion is appropriate.

math   Statistics-And-Probability   
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Let pi the proportion of women had babies with low birth weight and p2 the proportion of women with a history of premature labor had babies with low birth weight To test, whether proportion of babies born with low birth weight is higher for women with a history of premature labor i.e. p1 < p2or p1 p2<0 the null hypothesis would be Ho: p1 p2 0 against the alternative hypothesis Ha: p1-p2 < 0 Test statistic is given by We have, p1-0.26, p2-0.60, x-41, X2-18, n1-159 and n2-30 2 4180.312169312 n1+n2 159+30 ..Pooled proportion Now plug the values in above formula 0.26-0.60 03122(1-0.3122) (159+30 159 T 30 0.34 0.092237514 -3.686135764 p-value P(z < -3.6861) Since this is two tailed test (HA is with< sign) We can calculated P(z < -3.6861) using NORM.S.DIST(-3.6861, TRUE) excel function which gives 0.000113842 Hence, p-value 0.000113842 Since, p-value < 0.01 (1% level of significance) we reject null hypothesis and accept alternative That means (p1 < p2). So, the data provide evidence that the proportion of babies born with low birth weight is higher for women with a history of premature labor

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