Question

Most married couples have two or three personality preferences in common. A random sample of 379 married couples found that 134 had three preferences in common. Another random sample of 573 couples showed that 215 had two personality preferences in common. Let Pi 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. (a) Find a 90% confidence interval for pi -p2. (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.

Answer 1

Here, we have M: 379 2 = 134 Viñ . 379 Me = 573 x : 418 Pa to the ceremony = 0.375 a) At gox Contidence interval, .012= 0.05 0:1-0.905 0.10 Zerifical = 1.645 90v confidence interval for 18, -Pa) = 18, – P) + Borustica"/h, 1-2), 31-2) = (0.359-0379) + 1.646 * 0:35961-0 354) 0.3791-0379 :-0.021 + 0.05234 :-0.07334, 0.03134 -|-0.073, 0.031) Round to three decimal places A / 379 573

lower limit: 5-0073 | upper limit : 10.031 by Because, the interval contains both positive and negative numbers, we can not say that a higher Proportion of married couples have three personality Preference in common. 80, correct option-