Chapter 11: Q. 11.113 (page 477)

Folic Acid and Birth Defects. Refer to Exercise 11.107 and determine and interpret a $98 %$ confidence interval for the difference between the rates of major birth defects for babies born to women who have taken folic acid and those born to women who have not.

Short Answer

Expert verified

There is $98 %$ interval for the difference between the proportions is $(- 0.0188, 0.008$ )

Step by step solution

Given Information

The given values are,

$x_{1} = 35, n_{1} = 2701, x_{2} = 47, n_{2} = 2052, α = 0.02 .$

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,

$z = \frac{{\tilde{p}}_{1} - {\tilde{p}}_{2}}{\sqrt{{\tilde{p}}_{p} (1 - {\tilde{p}}_{p})} \sqrt{\frac{1}{n_{1}} + \frac{1}{n_{2}}}}$

The value of ${\tilde{p}}_{1}$ is calculated as,

${\tilde{p}}_{1} = \frac{x_{1}}{n_{1}} = \frac{35}{2701} = 0.013$

The value of ${\tilde{p}}_{2}$ is calculated as,

${\tilde{p}}_{2} = \frac{x_{2}}{n_{2}} = \frac{47}{2052} = 0.022$

Calculate the value of $z_{\frac{a}{2}}$ with $98 %$ confidence level is.

$z_{\frac{a}{2}} = z_{0.2 / 2}$

$= z_{0.01} = 2.326$

The $98 %$ confidence interval is.

$= (0.013 - 0.022) \pm 2.326 \sqrt{\frac{0.013 (1 - 0.013)}{2701} + \frac{0.022 (1 - 0.022)}{2052}}$

= - 0.009 \pm 0.0098

Therefore, there is $98 %$ interval for the difference between the proportion is $(- 0.0188, 0.008)$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Folic Acid and Birth Defects. Refer to Exercise 11.107 and determine and interpret a $98 %$ confidence interval for the difference between the rates of major birth defects for babies born to women who have taken folic acid and those born to women who have not.

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Folic Acid and Birth Defects. Refer to Exercise 11.107 and determine and interpret a 98% confidence interval for the difference between the rates of major birth defects for babies born to women who have taken folic acid and those born to women who have not.

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Folic Acid and Birth Defects. Refer to Exercise 11.107 and determine and interpret a $98 %$ confidence interval for the difference between the rates of major birth defects for babies born to women who have taken folic acid and those born to women who have not.