Allen’s hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther. A small group of 15 Allen’s hummingbirds has been under study in Arizona. The average weight for these birds is  = 3.15 grams. Based on previous studies, we can assume that the weights of Allen’s hummingbirds have a normal distribution, with σ = 0.33 gram.
(a) Find an 80% confidence interval for the average weight of Allen’s hummingbirds in the study region. What is the margin of error?
(b) What conditions are necessary for your calculations?
(c) Compare your results in the context of this problem.
(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.08 for the mean weight of the hummingbirds.