Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 15 Allen's

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Allen's hummingbird (Selasphorus sasin) has been studied by
zoologist Bill Alther.† Suppose a small group of 15 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 𝜎 = 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.) lower limit
upper limit margin of error
(b) What conditions are necessary for your calculations? (Select
all that apply.) n is large uniform distribution of weights normal
distribution of weights 𝜎 is unknown 𝜎 is known
(c) Interpret your results in the context of this problem. We
are 80% confident that the true average weight of Allen's
hummingbirds falls within this interval. The probability that this
interval contains the true average weight of Allen's hummingbirds
is 0.80. We are 20% confident that the true average weight of
Allen's hummingbirds falls within this interval. The probability
that this interval contains the true average weight of Allen's
hummingbirds is 0.20.
(d) Find the sample size necessary for an 80% confidence level
with a maximal margin of error E = 0.12 for the mean weights of the
hummingbirds. (Round up to the nearest whole number.)