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 lists the following weights of adult gray wolves from two regions in Old Mexico.

Chihuahua region: x₁ variable in pounds

Durango region: x₂ variable in pounds

(a) Use a calculator with mean and standard deviation keys to verify that x̅₁ = 75.80 pounds, s₁ = 8.32 pounds, x̅₂ = 66.83 pounds, and s₂ = 8.87 pounds.

(b) Check Requirements Assuming that the original distribution of the weights of wolves are mound-shaped and symmetric, what distribution can be used to approximate the x̅₁ – x̅₂ distribution? Explain.

(c) Let m₁ be the mean weight of the population of all gray wolves in the Chihuahua region. Let m₂ be the mean weight of the population of all gray wolves in the Durango region. Find an 85% confi­dence interval for m₁ – m₂.

(d) Interpretation 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 85% level of confi­dence, what can you say about the comparison of the average weight of gray wolves in the Chihuahua region with the average weight of gray wolves in the Durango region?

86 75 970 79 80 68 7 74 64 68 72 79 68 77 89 62 55 68 68 59 63 66 58 54 7159 67