A random sample of 388 married couples found that 284 had two or more personality preferences in common. In another random sample of 560 married couples, it was found that only 24 had no preferences in common. Let \( p_1 \) be the population proportion of all married couples who have two or more personality preferences in common. Let \( p_2 \) be the population proportion of all married couples who have no personality preferences in common.**(a)** Find a 90% confidence interval for \( p_1 - p_2 \). (Use 3 decimal places.)- Lower limit: [Input box]- Upper limit: [Input box]**(b)** Explain the meaning of the confidence interval in part (a) in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you (at the 90% confidence level) about the proportion of married couples with two or more personality preferences in common compared with the proportion of married couples sharing no personality preferences in common?- [ ] We can not make any conclusions using this confidence interval.- [ ] Because the interval contains only negative numbers, we can say that a higher proportion of married couples have no personality preferences in common.- [ ] Because the interval contains both positive and negative numbers, we can not say that a higher proportion of married couples have two or more personality preferences in common.- [ ] Because the interval contains only positive numbers, we can say that a higher proportion of married couples have two or more personality preferences in common.

Answered: fied couples who have two or more…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

A random sample of 388 married couples found that 284 had two or more personality preferences in common. In another random sample of 560 married couples, it was found that only 24 had no preferences in common. Let \( p_1 \) be the population proportion of all married couples who have two or more personality preferences in common. Let \( p_2 \) be the population proportion of all married couples who have no personality preferences in common.

**(a)** Find a 90% confidence interval for \( p_1 - p_2 \). (Use 3 decimal places.)

- Lower limit: [Input box]
- Upper limit: [Input box]

**(b)** Explain the meaning of the confidence interval in part (a) in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you (at the 90% confidence level) about the proportion of married couples with two or more personality preferences in common compared with the proportion of married couples sharing no personality preferences in common?

- [ ] We can not make any conclusions using this confidence interval.
- [ ] Because the interval contains only negative numbers, we can say that a higher proportion of married couples have no personality preferences in common.
- [ ] Because the interval contains both positive and negative numbers, we can not say that a higher proportion of married couples have two or more personality preferences in common.
- [ ] Because the interval contains only positive numbers, we can say that a higher proportion of married couples have two or more personality preferences in common.

Expert Solution

Step 1: Part a

Given information:
Sample 1:
- Sample size (): 388
- Couples with two or more personality preferences in common in Sample 1 (): 284

Sample 2:
- Sample size (): 560
- Couples with no personality preferences in common in Sample 2 (): 24

We'll calculate the sample proportions ( and ) for both samples:

Now, let's calculate the critical value () for a 90% confidence interval. For a 90% confidence interval, .

Next, we'll calculate the standard error of the difference in proportions ():

Calculating :

Now, let's calculate the margin of error ():

Now, we can construct the confidence interval for :

Lower Limit:

Upper Limit:

The 90% confidence interval for is approximately (0.6108, 0.7652).

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS