Homework Help is Here – Start Your Trial Now!
Math
Statistics
fied couples who have two or more personality preferences in common. Let, proportion of all married couples who have no personality preferences in common. USE SALT (a) Find a 90% confidence interval for P₁ - P₂. (Use 3 decimal places.) lower limit upper limit (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 negat negative numbers? What does this tell you (at the 90% confidence level) about the proportion of married couples with two or more personality prefere with the proportion of married couples sharing no personality preferences in common? We can not make any conclusions using this confidence interval

fied couples who have two or more personality preferences in common. Let, proportion of all married couples who have no personality preferences in common. USE SALT (a) Find a 90% confidence interval for P₁ - P₂. (Use 3 decimal places.) lower limit upper limit (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 negat negative numbers? What does this tell you (at the 90% confidence level) about the proportion of married couples with two or more personality prefere with the proportion of married couples sharing no personality preferences in common? We can not make any conclusions using this confidence interval

MATLAB: An Introduction with Applications
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
icon
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.
Transcribed Image Text: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).


steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
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