Question

Most married couples have two or three personality preferences
in common. A random sample of 362 married couples found that 140
had three preferences in common. Another random sample of
564couples showed that 220 had two personality preferences in
common. Let *p*_{1} be the population proportion of
all married couples who have three personality preferences in
common. Let *p*_{2} be the population proportion of
all married couples who have two personality preferences in
common.

(a) Find a 95% confidence interval for *p*_{1} –
*p*_{2}. (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 95% 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

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A random sample of 380 married couples found that 280 had two or
more personality preferences in common. In another random sample of
578 married couples, it was found that only 24 had no preferences
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of all married couples who have two or more personality preferences
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of all married couples who have no personality preferences in
common.
(a) Find a 90% confidence interval for...

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