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 ? = 0.22gram.

(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.)

? is known? is unknownn islargeuniform distribution of weightsnormal distribution ofweights

(c)

Interpret your results in the context of this problem.

There is an 80% chance that the interval is one of the intervalscontaining the true average weight of Allen's hummingbirds in thisregion.There is a 20% chance that the interval is one of theintervals containing the true average weight of Allen'shummingbirds in this region.    The probabilityto the true average weight of Allen's hummingbirds is equal to thesample mean.The probability that this interval contains the trueaverage weight of Allen's hummingbirds is 0.20.The probability thatthis interval contains the true average weight of Allen'shummingbirds is 0.80.

(d)

Find the sample size necessary for an 80% confidence level witha maximal margin of error E = 0.10 for the mean weights ofthe hummingbirds. (Round up to the nearest whole number.)

hummingbirds