3. -12.5 points 12 7.4.017 My Notes Ask Your A random sample of 366 married coup

Question

3. -12.5 points 12 7.4.017 My Notes Ask Your A random sample of 366 married couples found that 284 had two or more personality preferences in common. In another random sample of 584 married couples, it was found that only 26 had no preferences in common. Let p1 be the population proportion of all married couples who have two or more personality preferences in common. Let p2 be the population proportion of all married couples who have no personality preferences in common. (a) Find a 99% confidence interval for pi-p> (Use 3 decimal places.) lower limit upper limit context of this problem. Does the confidence interval contain all does this tell you (at the 99% confidence level) about the proportion of compared with the proportion of married couples sharing no personality (b) Explain the meaning of the confidence interval in part (a) in the positive, all negative, or both positive and negative numbers? What married couples with two or more personality preferences in common 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 only positive numbers, we can say that a higher proportion of married couples have two or more 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 We can not make any conclusions using this confidence interval Need Help? Readit

Explanation / Answer

> table = matrix(c(284,82,26,558), nrow = 2, ncol=2)

> prop.test(x = table, conf.level = 0.99, correct = FALSE)

2-sample test for equality of proportions without continuity correction

data: table

X-squared = 547.56, df = 1, p-value < 2.2e-16

alternative hypothesis: two.sided

99 percent confidence interval:

0.7350643 0.8409438

sample estimates:

prop 1 prop 2

0.916129 0.128125

THUS:

(a)

The 99% confidence interval is:

LOWER LIMIT - 0.735

UPPER LIMIT - 0.841

(b)

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.

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