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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

Solutions

Expert Solution

Values ( X ) Σ ( Xi- X̅ )2 Values ( Y ) Σ ( Yi- Y̅ )2
86 104.04 68 1.3612
75 0.64 72 26.6948
91 231.04 79 148.0286
70 33.64 68 1.3612
79 10.24 77 103.3618
80 17.64 89 491.3626
68 60.84 62 23.3608
71 23.04 55 140.027
74 3.24 68 1.3612
64 139.24 68 1.3612
59 61.3606
63 14.6942
66 0.6944
58 78.0272
54 164.6936
71 17.36
59 61.3606
67 0.0278
Total 758 623.6 1203 1336.5002

Mean X̅ = Σ Xi / n
X̅ = 758 / 10 = 75.8
Sample Standard deviation SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 623.6 / 10 -1 ) = 8.32

Mean Y̅ = ΣYi / n
Y̅ = 1203 / 18 = 66.83
Sample Standard deviation SY = √ ( (Yi - Y̅ )2 / n - 1 )
SY = √ ( 1336.5002 / 18 -1) = 8.87

part a)

X1 = 75.8

S1 = 8.32

X2 = 66.83

S2 = 8.87

Part b)

Confidence interval :-

t(α/2, DF) = t(0.01 /2, 19 ) = 2.861



DF = 19


Lower Limit =
Lower Limit = -0.65
Upper Limit =
Upper Limit = 18.58
99% Confidence interval is ( -0.65 , 18.58 )


milcah answered 4 months ago
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