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