A random sample of 370 married couples found that 286 had two or more personality preferences in common. In another random sample of 572 married couples, it was found that only 30 had no preferences in common. Let p, be the population proportion of all married couples who have two or more personality preferences in common. Let p, be the population proportion of all married couples who have no personality preferences in common. n USE SALT (a) Find a 90% confidence interval for p, - P3. (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 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? O Because the interval contains only negative numbers, we can say that a higher proportion of married couples have no personality preferences in common. O 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. O 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. O we can not make any conclusions using this confidence interval.
A random sample of 370 married couples found that 286 had two or more personality preferences in common. In another random sample of 572 married couples, it was found that only 30 had no preferences in common. Let p, be the population proportion of all married couples who have two or more personality preferences in common. Let p, be the population proportion of all married couples who have no personality preferences in common. n USE SALT (a) Find a 90% confidence interval for p, - P3. (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 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? O Because the interval contains only negative numbers, we can say that a higher proportion of married couples have no personality preferences in common. O 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. O 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. O we can not make any conclusions using this confidence interval.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![A random sample of 370 married couples found that 286 had two or more personality preferences in common. In another random sample of 572 married couples, it was found that only 30 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.
1. **(a) Find a 90% confidence interval for \( p_1 - p_2 \). (Use 3 decimal places.)**
- Lower limit: [input box]
- Upper limit: [input box]
2. **(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?**
- ○ 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 cannot 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.
- ○ We cannot make any conclusions using this confidence interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a8d585f-99dd-4e5d-b593-c7eaddfe8ce4%2F5ec3a310-7259-464e-9afd-a8b3c9e2ed3c%2Fa9cwm4_processed.png&w=3840&q=75)
Transcribed Image Text:A random sample of 370 married couples found that 286 had two or more personality preferences in common. In another random sample of 572 married couples, it was found that only 30 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.
1. **(a) Find a 90% confidence interval for \( p_1 - p_2 \). (Use 3 decimal places.)**
- Lower limit: [input box]
- Upper limit: [input box]
2. **(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?**
- ○ 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 cannot 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.
- ○ We cannot make any conclusions using this confidence interval.
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