Question

Allen's hummingbird (*Selasphorus sasin*) has been
studied by zoologist Bill Alther.† Suppose a small group of 16
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* = 0.34
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.)

*σ* is unknown*n* is largeuniform distribution of
weightsnormal distribution of weights*σ* is known

(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.

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 0.80.

(d) Find the sample size necessary for an 80% confidence level with
a maximal margin of error *E* = 0.11 for the mean weights of
the hummingbirds. (Round up to the nearest whole number.)

how many hummingbirds

Answer #1

Average, = 3.15 grams

Standard deviation, = 0.34 grams

n = 16

The sampling distribution of the sample mean of weight's of Allen's hummingbirds follows Normal distribution with Mean = 3.15 grams and Standard deviation = 0.34/√16 = 0.085 grams

(a) Corresponding to 80% confidence interval, the critical z score = 1.282

Margin of error = z*SE = 1.282*0.085 = 0.109

Lower limit = 3.15 - 0.109 ≈ 3.04 grams

upper limit = 3.15 + 0.109 ≈ 3.26 grams

Margin of error = 0.11 grams

(b) The necessary conditions are:

Normal distribution of weights

is known

(c) We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval

(d) E = 0.11

-> 1.282*0.34/√n = 0.11

-> n = 15.7 ≈ 16

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 σ = 0.40 gram.
(a) Find an 80% confidence interval for the average weights of
Allen's hummingbirds in the study region. What is the margin of...

Allen's hummingbird (Selasphorus sasin) has been
studied by zoologist Bill Alther.† Suppose a small group of 18
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 = 0.32
gram.
(a) Find an 80% confidence interval for the average weights of
Allen's hummingbirds in the study region. What is the margin of...

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 σ = 0.30 gram.
1. Find an 80% confidence interval for the average weights of
Allen's hummingbirds in the study region. What is the margin of...

Allen's hummingbird (Selasphorus sasin) has been
studied by zoologist Bill Alther.† Suppose a small group of 12
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 = 0.26
gram.
(a) Find an 80% confidence interval for the average weights of
Allen's hummingbirds in the study region. (Round your answers to
two...

Allen's hummingbird (Selasphorus sasin) has been
studied by zoologist Bill Alther.† Suppose a small group of 10
Allen's hummingbirds has been under study in Arizona. The average
weight for these birds is xbar = 3.15 grams. Based on
previous studies, we can assume that the weights of Allen's
hummingbirds have a normal distribution, with σ = 0.20
gram.
(a) Find an 80% confidence interval for the average weights of
Allen's hummingbirds in the study region. What is the margin of...

Allen's hummingbird (Selasphorus sasin) has been
studied by zoologist Bill Alther.† Suppose a small group of 14
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 = 0.36
gram.
(a) Find an 80% confidence interval for the average weights of
Allen's hummingbirds in the study region. What is the margin of...

Allen's hummingbird (Selasphorus sasin) has been
studied by zoologist Bill Alther.† Suppose a small group of 20
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 = 0.26
gram.
(a) Find an 80% confidence interval for the average weights of
Allen's hummingbirds in the study region. What is the margin of...

Allen's hummingbird (Selasphorus sasin) has been
studied by zoologist Bill Alther.† Suppose a small group of 18
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 = 0.22
gram.
(a) Find an 80% confidence interval for the average weights of
Allen's hummingbirds in the study region. What is the margin of...

Allen's hummingbird (Selasphorus sasin) has been
studied by zoologist Bill Alther.† Suppose a small group of 17
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 = 0.24
gram.
(a) Find an 80% confidence interval for the average weights of
Allen's hummingbirds in the study region. What is the margin of...

Allen's hummingbird (Selasphorus sasin) has been studied by
zoologist Bill Alther.† Suppose a small group of 12 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 = 0.36 gram. (a) Find an 80% confidence
interval for the average weights of Allen's hummingbirds in the
study region. What is the margin of...

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