Question

Allen's hummingbird (*Selasphorus sasin*) has been
studied by zoologist Bill Alther.† Suppose a small group of 19
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 *?* = 0.22
gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. (Round your answers to two decimal places.)

lower limit ______ | |

upper limit _______ | |

margin of error _______ |

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

________ hummingbirds

Answer #1

Given in the question

N= 19 so degree of freedom = 18

Sample mean = 3.15

Population standard deviation = 0.22

alpha= 0.2 and alpha/2 = 0.1

so talpha/2 at 0.1 and df=18 is 1.330

So confidence interval is

3.15+/-1.330*(0.22/sqrt(19))

3.15+/-1.330*0.22/4.3588

Lower limit=3.15 - 1.330*0.22/4.3588 = 3.15-0.067128 = 3.0828

Upper Limit = 3.15 + 1.330*0.22/4.3588 = 3.15+0.067128 =
3.2117128

Margin of error = 1.330*0.22/sqrt(19) = 0.067128

Solution(2):

Margin of error = Zalpha/2*0.22/sqrt(n)

0.11 = 1.28*0.22/sqrt(n)

sqrt(n)=1.28*0.22/0.11 =

n= 2.56*2.56 = 6.5536 or 7

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 = 0.22
gram.
Find the sample size necessary for an 80% confidence level with a
maximal margin of error E = 0.16 for the mean...

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 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.
Find the sample size necessary for an 80% confidence level with
a maximal margin of error E = 0.11 for the mean...

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 = 0.34
gram.
(a) Find an 80% confidence interval for the average weights of
Allen's hummingbirds in the study region. What is the margin of...

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 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 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 = 0.26 gram.
(d) Find the sample size necessary for an 80% confidence level
with a maximal margin of error E = 0.06 for the
mean...

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 = 0.28 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 ? = 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 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 = 0.32 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 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 = 0.20 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 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 = 0.30
gram.
a.) When finding an 80% confidence interval, what is the
critical value for confidence level? (Round your answers to two
decimal places.)...

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