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Folic Acid and Birth Defects. For several years, evidence had been mounting that folic acid reduces major birth defects. A. Creizel and I. Dudas of the National Institute of Hygiene in Budapest directed a study that provided the strongest evidence to date. Their results were published in the paper "Prevention of the First Occurrence of Neural-Tube Defects by Periconceptional Vitamin Supplementation" (New England Journal of Medicine, Vol. 327(26). p. 1832 ). For the study, the doctors enrolled women prior to conception and divided them randomly into two groups. One group, consisting of 2701 women, took daily multivitamins containing $0.8$mg of folic acid; the other group, consisting of 2052 women, received nay A. Creizel and L. Duxlas of the National Institute of Hygiene i) Budapest directed a study that provided the strongest evidence to date Their results were published in the paper "Prevention of the Firs Occurrence of Neural-Tube Defects by Periconceptional Vitamin Supplementation" (New England Journal of Medicine, Vol. 327(26). p. 1832 ). For the study, the doctors enrolled women prior to conception and divided them randomly into two groups. One group, consisting of 2701 women, took daily multivitamins containing $0.8$mg of folic acid; the other group. consisting of 2052 women, received only trace elements. Major birth defects occurred in 35 cases when the women took folic acid and in 47 cases when the women did not.

a. At the $1\%$significance level, do the data provide sufficient evidence to conclude that women who take folic acid are at lesser risk of having children with major birth defects?

b. Is this study a designed experiment or an observational study? Explain your answer.

c. In view of your answers to parts (a) and (b), could you reasonably conclude that taking folic acid causes a reduction in major birth defects? Explain your answer.

Step by step solution

01

Part(a) Step 1: Given Information

The given values are,

$$\begin{gathered} x_1=35, \\ {n}_1=2701, \\ {x}_2=47, \\ {n}_2=2052, \\ \mathrm{Î\pm }=0.01 \end{gathered}$$

02

Part(a) Step 2: Explanation

The formula for ${\tilde{p}}_1$is given by,

${\tilde{p}}_1=\frac{x_1}{n_1}$

The formula for ${\tilde{p}}_2$is given by,

${\tilde{p}}_2=\frac{x_2}{n_2}$

The formula for $z$is given by,

$z=\frac{{\tilde{p}}_1-{\tilde{p}}_2}{\sqrt{{\tilde{p}}_p\left(1-{\tilde{p}}_p\right)}\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

The formula for ${\tilde{p}}_p$is given by,

${\tilde{p}}_p=\frac{x_1+x_2}{n_1+n_2}$

The value of $n_1-x_1$is calculated as,

$$\begin{gathered} n_1-x_1=2701-35 \\ =2666 \end{gathered}$$

The value of $n_2-x_2$is calculated as,

$$\begin{gathered} n_2-x_2=2052-47 \\ =2005 \end{gathered}$$

The values $x_1,\left(n_1-x_1\right),x_2$, and $\left(n_2-x_2\right)$are all greater than 5 .

The value of ${\tilde{p}}_1$is calculated as,

${\tilde{p}}_1=\frac{x_1}{n_1}$

$$\begin{gathered} =\frac{35}{2701} \\ =0.013 \end{gathered}$$

The value of ${\tilde{p}}_2$is calculated as,

$$\begin{gathered} {\tilde{p}}_2=\frac{x_2}{n_2} \\ =\frac{47}{2052} \\ =0.023 \end{gathered}$$

The value of ${\tilde{p}}_p$is calculated as,

$$\begin{gathered} {\tilde{p}}_p=\frac{x_1+x_2}{n_1+n_2} \\ =\frac{35+47}{2701+2052} \\ =0.017 \\ \tilde{q}=1-{\tilde{p}}_p \\ =1-0.017 \\ =0.983 \end{gathered}$$

The value of $z$is calculated as,

$z=\frac{{\tilde{p}}_1-{\tilde{p}}_2}{\sqrt{\tilde{p}\left(1-{\tilde{p}}_p\right)}\sqrt{\frac{1}{n_1}+\frac{1}{m_2}}}$

$$\begin{gathered} =\frac{0.013-0.023}{\sqrt{0.017(1-0.017)}\left(\sqrt{\frac{1}{2701}+\frac{1}{2052}}\right)} \\ =-2.67 \end{gathered}$$

We concluded that the data provide sufficient evidence to conclude that women who take folic acid have a lower risk of having children with major birth defects (calculated $z-$value (-2.67) is less than the initial value (=-2.326), 1% level of significance).

As a result, at a 1% level of significance, the data provide enough evidence to conclude that women who take folic acid are less likely to have children with major birth defects.

03

Part(b) Step 1: Given Information

The given values are,

$$\begin{gathered} x_1=35, \\ {n}_1=2701, \\ {x}_2=47, \\ {n}_2=2052, \\ \mathrm{Î\pm }=0.01 \end{gathered}$$

04

Part(b) Step 2: Explanation

Using the previously solved solution in the preceding section.

This is a planned experiment study in which relevant information about the statistical hypothesis under study is obtained from the experiment and the data is statistically analyzed.

As a result, this is a planned experiment study.

05

Part(c) Step 1: Given Information

The given values are,

$$\begin{gathered} x_1=35, \\ {n}_1=2701, \\ {x}_2=47, \\ {n}_2=2052, \\ \mathrm{Î\pm }=0.01 \end{gathered}$$

06

Part(c) Step 2: Explanation

Using the previously solved solution in the preceding section.

Yes, because statistical significance can be interpreted as a causal relationship in a well-designed experiment.

As a result, it is reasonable to interpret statistical significance as indicating a causal relationship.

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