Question

Most married couples have two or three personality preferences in common. A random sample of 374 married couples found that 128 had three preferences in common. Another random sample of 558 couples showed that 200 had two personality preferences in common. Let p₁ 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 95% confidence interval for p₁ – p₂. (Use 3 decimal places.)

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(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)?

A. Because the interval contains only positive numbers, we can say that a higher proportion of married couples have three personality preferences in common.

B. 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.

C. We can not make any conclusions using this confidence interval.

D.Because the interval contains only negative numbers, we can say that a higher proportion of married couples have two personality preferences in common.

A random sample of 25 adult male wolves from the Canadian Northwest Territories gave an average weight x₁ = 97.4 pounds with estimated sample standard deviation s₁ = 7.2 pounds. Another sample of 23 adult male wolves from Alaska gave an average weight x₂ = 90.2 pounds with estimated sample standard deviation s₂ = 6.7 pounds.(a) Categorize the problem below according to parameter being estimated, proportion p, mean μ, difference of means μ₁ – μ₂, or difference of proportions p₁ – p₂. Then solve the problem.

A. p

B. μ   

C. μ₁ – μ₂

_D.p₁ – p₂

(b) Let μ₁ represent the population mean weight of adult male wolves from the Northwest Territories, and let μ₂ represent the population mean weight of adult male wolves from Alaska. Find a 95% confidence interval for μ₁ – μ₂. (Use 1 decimal place.)

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(c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 95% level of confidence, does it appear that the average weight of adult male wolves from the Northwest Territories is greater than that of the Alaska wolves?

A. Because the interval contains only positive numbers, we can say that Canadian wolves weigh more than Alaskan wolves.

B. Because the interval contains both positive and negative numbers, we can not say that Canadian wolves weigh more than Alaskan wolves.

C. We can not make any conclusions using this confidence interval.

D.Because the interval contains only negative numbers, we can say that Alaskan wolves weigh more than Canadian wolves.

Answer 1

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