Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 17 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 = 0.26 gram.
(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. (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.)
σ is known
n is large
normal distribution of weights
σ is unknown
uniform distribution of weights
(d) Find the sample size necessary for an 80% confidence level with a maximal error of estimate E = 0.12 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
= _______ hummingbirds?