Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.Suppose a small group of12Allen's hummingbirds has been under study in Arizona. The average weight for these birds isx= 3.15 grams.Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with=0.34gram.

(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.)

• is known
• is unknown
• nis large
• uniform distribution of weights
• normal distribution of weights

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

• 1. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.
• 2. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.
• 3. We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval.
• 4. We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of errorE=0.13for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

• _______hummingbirds