Allen's hummingbird (Selasphorus sasin) has been studied by zoologist eill Althecit Suppose a
smail group of 14 Alen's hummingbirds has been under study in Avizona. Tbe average weight
for these birds is x=3.15 orams. Based on previous studies, we can assume that the weights of
Allen's hummingbirds have a narmal distribution, with o = 0.40 gram. When finding an 80%
confidence interval, what is the critical value for confidence lewer? (Glue vour answer to two
decimal places.) zc (a) Find an 80%6 confidence interval for the average weights of Allen's
hummingbirds in the study region. What is the margin of errof? (Rocnd your ansners to twie
decimal places.) lower limit upper limit maroin of ecroe (b) What condlitions are necessary for
your calculations? (5elect all that apply. a is unkown uniform distribution of weights normal
distribution of weichts n is large is is known (c) tnterpret your results in the context of this
problem. the probabiaty that this interyal contains the true averape weight of Alleois
humringbirds is 0.20 . We are 20% confidest that the true average weight of Alien's
humemingbirds fals within this interval. The probability that this interval contains the true
average weight of Allen's hummingtirds is 0.00. We are soes confident that the true average
weight of Allen's hummingbirds falls within this interval. (d) Which equation is used to find the
sample size n for estimating is when o is known? n=EFen=(E2ae)2n=n=(zcE)2 Find the sample
size necessary for an so% contidence level with a maximal margin of arres E0.14 for the mean
weights of the hummingbirds. (Round up to the nearest whole numbec.) hummingbirds