Allen\'s hummingbird ( Selasphorus sasin ) has been studied by zoologist Bill Al

Question

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 10 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with = 0.24 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

Explanation / Answer

Sample size,n = 10
average weight, x-bar = 3.15 grams
Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with = 0.24 gram.
a)

s.e. = / n = 0.24 / 10 = 0.07
Z = 1.282 at 80% confidence
margin of error, E = s.e.× Z = 0.07 × 1.282 = 0.08974

lower limit = x-bar - E = 3.15 - 0.08974 = 3.0602
upper limit = x-bar + E = 3.15 + 0.08974 = 3.2397
margin of error = 0.08974
80% Confidence Interval = ( 3.0602 , 3.2397 )

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