We want to compare the ear lengths of female African and Indian elephants. A ran
ID: 3159156 • Letter: W
Question
We want to compare the ear lengths of female African and Indian elephants. A random sample of female African elephants has the following ear lengths, in centimeters: 104, 98, 110, 81, 111, 123. A random sample of female Indian elephants has the following ear lengths: 82, 71, 65, 57, 93, 86, 77. We assume both populations of ear lengths are approximately normal. Find a 95% confidence interval for the difference between female African and female Indian elephants’ ear lengths. Assume the population standard deviations are not equal.
Explanation / Answer
Calculating the means of each group,
X1 = 104.5
X2 = 75.85714286
Calculating the standard deviations of each group,
s1 = 14.20915198
s2 = 12.4690092
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 6
n2 = sample size of group 2 = 7
Thus, df = n1 + n2 - 2 = 11
Also, sD = 7.474013939
For the 0.95 confidence level, then
alpha/2 = (1 - confidence level)/2 = 0.025
hence,
t(alpha/2) = 2.20098516
Thus,
lower bound = [X1 - X2] - t(alpha/2) * sD = 12.19266338
upper bound = [X1 - X2] + t(alpha/2) * sD = 45.09305091
Thus, the confidence interval is
( 12.19266338 , 45.09305091 ) [ANSWER]
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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!
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