Chapter 11: Q. 11.117 (page 477)

Body Mass Index. Refer to Exercise 11.111 and find and interpret a $90 %$ confidence interval for the difference between the percentages of adults in the Iwo degree categories who have an above healthy weight.

Short Answer

Expert verified

There is $90 %$ interval for the difference between the proportion is (-0.0064,0.0884)

Step by step solution

Given Information

The given values are,

$x_{1} = 386, n_{1} = 750, x_{2} = 237, n_{2} = 500, {\tilde{p}}_{1} = 0.515, {\tilde{p}}_{2} = 0.474$

Explanation

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}}}}

Calculate the value of $z_{\frac{a}{2}}$ with $90 %$ confidence level is $1.645$ .

The $98 %$ confidence interval is.

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

$= (- 0.0064, 0.0884)$

Therefore, there is $90 %$ interval for the difference between the proportion is $(- 0.0064, 0.0884)$

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.

Body Mass Index. Refer to Exercise 11.111 and find and interpret a $90 %$ confidence interval for the difference between the percentages of adults in the Iwo degree categories who have an above healthy weight.

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

Probability and Statistics

Logic and Functions

Decision Maths

Calculus

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Body Mass Index. Refer to Exercise 11.111 and find and interpret a 90% confidence interval for the difference between the percentages of adults in the Iwo degree categories who have an above healthy weight.

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

Probability and Statistics

Logic and Functions

Decision Maths

Calculus

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Body Mass Index. Refer to Exercise 11.111 and find and interpret a $90 %$ confidence interval for the difference between the percentages of adults in the Iwo degree categories who have an above healthy weight.