A random sample of 19 adult male wolves from the Canadian Northwest Territories gave an average weight x1 = 96.2 pounds with estimated sample standard deviation s1 = 5.5 pounds. Another sample of 23 adult male wolves from Alaska gave an average weight x2 = 88.4 pounds with estimated sample standard deviation s2 = 6.9 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. μ1 – μ2p p1 – p2μ (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.) lower limit upper limit (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? Because the interval contains only positive numbers, we can say that Canadian wolves weigh more than Alaskan wolves.Because the interval contains both positive and negative numbers, we can not say that Canadian wolves weigh more than Alaskan wolves. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that Alaskan wolves weigh more than Canadian wolves.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

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Chapter10: Statistics

Section: Chapter Questions

Problem 22SGR

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A random sample of 19 adult male wolves from the Canadian Northwest Territories gave an average weight x₁ = 96.2 pounds with estimated sample standard deviation s₁ = 5.5 pounds. Another sample of 23 adult male wolves from Alaska gave an average weight x₂ = 88.4 pounds with estimated sample standard deviation s₂ = 6.9 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.

μ₁ – μ₂p p₁ – p₂μ

(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.)

lower limit
upper limit

(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?

Because the interval contains only positive numbers, we can say that Canadian wolves weigh more than Alaskan wolves.Because the interval contains both positive and negative numbers, we can not say that Canadian wolves weigh more than Alaskan wolves. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that Alaskan wolves weigh more than Canadian wolves.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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