5. [-/0.27 Points] DETAILS BBUNDER A random sample of 366 married couples found that 300 had two or more personality preferences in common. In another random sample of 562 married couples, it was found that only 28 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. LO USE SALT (a) Find a 90% confidence interval for P1 7 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 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 both positive and negative numbers, we can not say that a higher proportion of married couples have two or more personality preferences in common. We can not make any conclusions using this confidence interval. 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. Because the interval contains only negative numbers, we can say that a higher proportion of married couples have no personality preferences in common. Need Help? Read It Watch It 6. [-/0.27 Points] DETAILS BBUNDERSTAT12 7.4.018.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Most married couples have two or three personality preferences in common. A random sample of 360 married couples found that 128 had three preferences in common. Another random sample of 552 couples showed that 204 had two personality preferences in common. Let p, be the population proportion of all married couples who have three personality preferences in common. Let p2 be the population proportion of all married couples who have two personality preferences in common. LO USE SALT (a) Find a 99% confidence interval for P1 - P2. (Use 3 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 99% 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. Need Help? Read It
