Question
Allen's hummingbird ( Selasphorus sasin ) has been studied by zoologist Bill Alther. Suppose a small group of 11 Allen's hummingbirds has been under study
Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther. Suppose a small group of 11 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with = 0.30 gram.
(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.)
-uniform distribution of weights
- is unknown
- is known normal distribution of weights is large.
(c)Interpret your results in the context of this problem.
-We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval.
-The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.
-The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.
-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 error E = 0.16 for the mean weights of the hummingbirds. (Round up to the nearest whole number.) hummingbirds
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