Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 11 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 ? = 0.32 gram. (a) Find an 80% confidence interval for the average weights of

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Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 11 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 ? = 0.32 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.)
lower limit     __
upper limit     __
margin of error     __

(b) What conditions are necessary for your calculations? (Select all that apply.)
A-n is large
B-? is unknown
C-? is know
D-nnormal distribution of weights
E-uniform distribution of weights

(c) MUTIPLE CHOICE  Interpret your results in the context of this problem.
A-We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval.
B-The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.
C-The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80. 
D-We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.08 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
 __hummingbirds
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