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A random sample of 366 married couples found that 286 had two ormore personality preferences in common. In another random sample of552 married couples, it was found that only 38 had no preferencesin common. Let p₁ be the population proportionof all married couples who have two or more personality preferencesin common. Let p₂ be the population proportionof all married couples who have no personality preferences incommon.

(a) Find a 90% confidence interval for p₁ –p₂. (Use 3 decimal places.)

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

Because the interval contains both positive and negativenumbers, we can not say that a higher proportion of married coupleshave two or more personality preferences in common.

We can not make any conclusions using this confidenceinterval.    

Because the interval contains only negative numbers, we can saythat a higher proportion of married couples have no personalitypreferences in common.

Because the interval contains only positive numbers, we can saythat a higher proportion of married couples have two or morepersonality preferences in common.