Answer Happy

Allen's hummingbird (Selasphorus sasin) has been studied by
zoologist Bill Alther.† Suppose a small group of 15 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 𝜎 = 0.30 gram. When finding an 80% confidence
interval, what is the critical value for confidence level? (Give
your answer to two decimal places.) zc =
(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.) 𝜎 is known n is large uniform distribution of
weights normal distribution of weights 𝜎 is unknown
(c) Interpret your results in the context of this problem. 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.
The probability that this interval contains the true average weight
of Allen's hummingbirds is 0.20. We are 80% confident that the true
average weight of Allen's hummingbirds falls within this
interval.
(d) Which equation is used to find the sample size n for
estimating 𝜇 when 𝜎 is known? n = z𝜎 𝜎 E 2 n = z𝜎 𝜎 E n = z𝜎 E 𝜎 2
n = z𝜎 E 𝜎 Find the sample size necessary for an 80% confidence
level with a maximal margin of error E = 0.09 for the mean weights
of the hummingbirds. (Round up to the nearest whole number.)