Do both short mcq problem 9Most married couples have two or three personality preferences in common. A random sampleof 377 married couples found that 130 had three preferences in common. Another random sampleof 569 couples showed that 217 had two personality preferences in common. Let pi be the populationproportion of all married couples who have three personality preferences in common. Let p₂ be thepopulation proportion of all married couples who have two personality preferences in common.(a) Find a 90% confidence interval for p-pz. (Round your answers to three decimal places.)lower limitupper limit(b) Examine the confidence interval in part (a) and explain what it means 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 about the proportion of married couples with three personality preferences incommon compared with the proportion of couples with two preferences in common (at the 90%confidence level)?Because the interval contains only positive numbers, we can say that a higher proportion of marriedcouples have three personality preferences in common. Because the interval contains both positiveand negative numbers, we can not say that a higher proportion of married couples have three personalitypreferences 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 marriedcouples have two personality preferences in common. Isabel Myers was a pioneer in the study of personality types. She identified four basic personalitypreferences that are described at length in the book Manual. A Guide to the Development and Use of theMyers-Briggs Type Indicator, by Myers and McCaulley.† Marriage counselors know that couples who havenone of the four preferences in common may have a stormy marriage.8A random sample of 373 married couples found that 291 had two or more personality preferences incommon. In another random sample of 572 married couples, it was found that only 18 had nopreferences in common. Let p, be the population proportion of all married couples who have two or morepersonality preferences in common. Let pz be the population proportion of all married couples who haveno personality preferences in common.(a)Find a 99% confidence interval for p₁ - P₂. (Round your answers to three decimal places.)lower limit(b)Explain the meaning of the confidence interval in part (a) in the context of this problem. Does theconfidence interval contain all positive, all negative, or both positive and negative numbers? What doesthis tell you (at the 99% confidence level) about the proportion of married couples with two or morepersonality preferences in common compared with the proportion of married couples sharing nopersonality preferences in common?upper limitBecause the interval contains only positive numbers, we can say that a higher proportion of marriedcouples have two or more personality preferences in common. Because the interval contains bothpositive and negative numbers, we can not say that a higher proportion of married couples have two ormore personality preferences in common. We can not make any conclusions using this confidenceinterval. Because the interval contains only negative numbers, we can say that a higher proportion ofmarried couples have no personality preferences in common.

Problem 8: First sample: Sample size n1=373 Number of successes x1=291 Second sample: Sample size…

Most married couples have two or three personality preferences in common. A random sample of 377 married couples found that 130 had three preferences in common. Another random sample of 569 couples showed that 217 had two personality preferences in common. Let p: be the population proportion of all married couples who have three personality preferences in common. Let p; be the population proportion of all married couples who have two personality preferences in common. (a) Find a 90% confidence interval for p-pz. (Round your answers to three decimal places.) lower limit upper limit (b) Examine the confidence interval in part (a) and explain what it means 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 about the proportion of married couples with three personality preferences in common compared with the proportion of couples with two preferences in common (at the 90% confidence level)? Because the interval contains only positive numbers, we can say that a higher proportion of married couples have three 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 three 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 two personality preferences in common.

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P