Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.Suppose a small group of14Allen's hummingbirds has been under study in Arizona. The average weight for these birds isx=3.30grams.Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with=0.30gram.

When finding an80% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.)

z_c=

(a)

Find an80% 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.)

is known.

uniform distribution of weights.

nis large.

normal distribution of weights.

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 0.8.

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 0.2.

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 sizenfor estimatingwhenis known?

n=

z_c

E

n=z_c

E

2

n=

z_cE

n=z_cE

2

Find the minimal sample size necessary for an80% confidence level with a maximal margin of errorE=0.07for the mean weights of the hummingbirds. (Round your answer to a whole number.)

hummingbirds=