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. (Round your answers to four decimal places.)
(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 an 80% confidence interval for 𝜇1 – 𝜇2. (Round your answers to two decimal places.)
(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 80% 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?