Allen's hummingbird (Selasphorus sasin) has beenstudied by zoologist Bill Alther.† Suppose a small group of 14Allen'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 = 0.20gram.

(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

(b)

What conditions are necessary for your calculations? (Select allthat apply.)

normal distribution of weightsn is largeuniformdistribution of weightsσ is unknownσ is known

(c)

Interpret your results in the context of this problem.

We are 20% confident that the true average weight of Allen'shummingbirds falls within this interval.The probability that thisinterval contains the true average weight of Allen's hummingbirdsis 0.80.     The probability that thisinterval contains the true average weight of Allen's hummingbirdsis 0.20.We are 80% confident that the true average weight ofAllen's hummingbirds falls within this interval.

(d)

Find the sample size necessary for an 80% confidence level witha maximal margin of error  E = 0.06 for the meanweights of the hummingbirds. (Round up to the nearest wholenumber.)