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David E. Brown is an expert in wildlife conservation. In his book The Wolf in the...

David E. Brown is an expert in wildlife conservation. In his book The Wolf in the Southwest: The Making of an Endangered Species (University of Arizona Press), he records the following weights of adult grey wolves from two regions in Old Mexico.

Chihuahua region: x1 variable in pounds

86 75 91 70 79
80 68 71 74 64

Durango region: x2 variable in pounds

68 72 79 68 77 89 62 55 68
68 59 63 66 58 54 71 59 67

(a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Use 2 decimal places.)

x1
s1
x2
s2


(b) Let μ1 be the mean weight of the population of all grey wolves in the Chihuahua region. Let μ2 be the mean weight of the population of all grey wolves in the Durango region. Find a 99% confidence interval for μ1 – μ2. (Use 2 decimal places.)

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 99% level of confidence, what can you say about the comparison of the average weight of grey wolves in the Chihuahua region with the average weight of grey wolves in the Durango region?

Because the interval contains only positive numbers, we can say that the mean weight of grey wolves is greater in the Chihuahua region.Because the interval contains only negative numbers, we can say that the mean weight of grey wolves is greater in the Durango region.    Because the interval contains both positive and negative numbers, we can not say that the mean weight of grey wolves is greater in the Chihuahua region.We can not make any conclusions using this confidence interval.

Solutions

Expert Solution

a)

b) The confidence interval for difference of means is

where are the t-value for the desired level of confidence and estimated standard error of difference between the means.

For our case, for confidence and degrees of freedom can be looked up to be equal to .

Estimated standard error can be calculated as

c) The range of the confidence interval comprises only of positive numbers. This suggests that the average weight of grey wolves is greater in the Chihuahua region as compared to those in the Durango region.

milcah answered 3 months ago
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