Allen's hummingbird (Selasphorus sasi) has been studied by zoologist x = 3.70 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with a = 0.32 gram. Suppose a small group of 12 Allen's hummingbirds has been under study in Arizona. The average weight for these birds When finding an 90% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.) Z₁ = (a) Find an 90% 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 Do is unknown Da is known On is large O normal distribution of weights (c) Interpret your results in the context of this problem. O The probability that this interval contains the true average weight of Allen's hummingbirds is 0.9. O We are 90% confident that the true average weight of Allen's hummingbirds falls within this interval. O We are 10% confident that the true average weight of Allen's hummingbirds falls within this interval. O The probability that this interval contains the true average weight of Allen's hummingbirds is 0.1.
Allen's hummingbird (Selasphorus sasi) has been studied by zoologist x = 3.70 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with a = 0.32 gram. Suppose a small group of 12 Allen's hummingbirds has been under study in Arizona. The average weight for these birds When finding an 90% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.) Z₁ = (a) Find an 90% 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 Do is unknown Da is known On is large O normal distribution of weights (c) Interpret your results in the context of this problem. O The probability that this interval contains the true average weight of Allen's hummingbirds is 0.9. O We are 90% confident that the true average weight of Allen's hummingbirds falls within this interval. O We are 10% confident that the true average weight of Allen's hummingbirds falls within this interval. O The probability that this interval contains the true average weight of Allen's hummingbirds is 0.1.
MATLAB: An Introduction with Applications
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Transcribed Image Text: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 = 3.70 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.32 gram.
When finding an 90% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.)
Zc =
(a) Find an 90% 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.)
O uniform distribution of weights
Do is unknown
Oo is known
On is large
O normal distribution of weights
(c) Interpret your results in the context of this problem.
O The probability that this interval contains the true average weight of Allen's hummingbirds is 0.9.
O We are 90% confident that the true average weight of Allen's hummingbirds falls within this interval.
O We are 10% confident that the true average weight of Allen's hummingbirds falls within this interval.
O The probability that this interval contains the true average weight of Allen's hummingbirds is 0.1.
(d) Which equation is used to find the sample size n for estimating u when σ is known?
μ
On=
On=
Z_O
E
ZE
b
n = ( ² - ² ) ²2
O
On-(²0)²
E
Find the minimal sample size necessary for an 90% confidence level with a maximal margin of error E = 0.11 for the mean weights of the hummingbirds. (Round your answer to a whole number.)
hummingbirds
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VIEWStep 2: Obtain the critical value for the 90% confidence interval.
VIEWStep 3: Obtain 90% confidence interval for the average weights of Allen’s hummingbirds in the study region
VIEWStep 4: Determine the conditions that are necessary for calculating the confidence interval.
VIEWStep 5: Interpret the confidence interval.
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