Allen's hummingbird (Selasphorus sasin) has beenstudied by zoologist Bill Alther.† Suppose a small group of 12Allen'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 limitupper limitmargin of error

(b)

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

σ is knownσ is unknownn islargenormal distribution of weightsuniform distribution ofweights

(c)

Interpret your results in the context of this problem.

There is a 20% chance that the interval is one of the intervalscontaining the true average weight of Allen's hummingbirds in thisregion.The probability that this interval contains the true averageweight of Allen's hummingbirds is0.20.    There is an 80% chance that theinterval is one of the intervals containing the true average weightof Allen's hummingbirds in this region.The probability that thisinterval contains the true average weight of Allen's hummingbirdsis 0.80.The probability to the true average weight of Allen'shummingbirds is equal to the sample mean.

(d)

Find the sample size necessary for an 80% confidence level witha maximal margin of error E = 0.09 for the mean weights ofthe hummingbirds. (Round up to the nearest whole number.)

hummingbirds