Allen's hummingbird (Selasphorus sasin) has been studied byzoologist Bill Alther.†Suppose a small group of 19 Allen'shummingbirds has been under study in Arizona. The average weightfor these birds is x = 3.15 grams. Based on previous studies, wecan assume that the weights of Allen's hummingbirds have a normaldistribution, with σ = 0.26 gram.
(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 knownσ is unknownnormal distribution ofweightsn is largeuniform distribution of weights
(c) Interpret your results in the context of this problem.
The probability to the true average weight of Allen'shummingbirds is equal to the sample mean.The probability that thisinterval contains the true average weight of Allen's hummingbirdsis 0.80.    There is an 80% chance that theinterval is one of the intervals containing the true average weightof Allen's hummingbirds in this region.There is a 20% chance thatthe interval is one of the intervals containing the true averageweight of Allen's hummingbirds in this region.The probability thatthis interval contains the true average weight of Allen'shummingbirds is 0.20.
(d) Find the sample size necessary for an 80% confidence level witha maximal margin of error E = 0.15 for the mean weights ofthe hummingbirds. (Round up to the nearest whole number.)
hummingbirds
