Allen's hummingbird (Selasphorus sasin) has beenstudied by zoologist Bill Alther.† Suppose a small group of 17Allen's hummingbirds has been under study in Arizona. The averageweight for these birds is x = 3.15 grams. Based onprevious studies, we can assume that the weights of Allen'shummingbirds have a normal distribution, with σ = 0.40gram.

(a) Find an 80% confidence interval for the average weights ofAllen's hummingbirds in the study region. What is the margin oferror? (Round your answers to two decimal places.)

lower limit _______
upper limit ______
margin of error _______

(b) What conditions are necessary for your calculations? (Selectall that apply.)

σ is unknownn is large

σ is known normal

distribution of weights

uniform distribution of weights

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true averageweight of Allen's hummingbirds is 0.20.There is an 80% chance thatthe interval is one of the intervals containing the true averageweight of Allen's hummingbirds in thisregion.    The probability that this intervalcontains the true average weight of Allen's hummingbirds is0.80.The probability to the true average weight of Allen'shummingbirds is equal to the sample mean.There is a 20% chance thatthe interval is one of the intervals containing the true averageweight of Allen's hummingbirds in this region.

(d) Find the sample size necessary for an 80% confidence level witha maximal margin of error E = 0.16 for the mean weights ofthe hummingbirds. (Round up to the nearest whole number.)
hummingbirds