Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.t 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 o = 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 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 normal distribution of weights O o is known On is large O o is unknown O uniform 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 0.20. O we are 80% confident that the true average weight of Allen's hummingbirds falls within this interval. O we are 20% 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 0.80. (d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.16 for the mean weights of the hummingbirds. (Round up to the nearest whole number.) hummingbirds
Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.t 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 o = 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 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 normal distribution of weights O o is known On is large O o is unknown O uniform 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 0.20. O we are 80% confident that the true average weight of Allen's hummingbirds falls within this interval. O we are 20% 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 0.80. (d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.16 for the mean weights of the hummingbirds. (Round up to the nearest whole number.) hummingbirds
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Allen’s Hummingbird Study**
Allen's hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther. A small group of 20 Allen's hummingbirds in Arizona was observed. The average weight for these birds is \(\bar{x} = 3.15\) grams. Previous studies suggest that the weights of Allen's hummingbirds follow a normal distribution, with \(\sigma = 0.32\) gram.
**(a) 80% Confidence Interval Calculation**
Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. Determine the margin of error. (Round answers to two decimal places.)
- Lower limit: [ ]
- Upper limit: [ ]
- Margin of error: [ ]
**(b) Necessary Conditions**
Select all necessary conditions for your calculations:
- [ ] Normal distribution of weights
- [ ] \(\sigma\) is known
- [ ] \(n\) is large
- [ ] \(\sigma\) is unknown
- [ ] Uniform distribution of weights
**(c) Interpretation of Results**
Interpret the results in the context of this problem:
- ( ) 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.
- ( ) 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) Sample Size for 80% Confidence with Maximum Margin of Error**
Find the sample size necessary for an 80% confidence level with a maximal margin of error \(E = 0.16\) for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
- [ ] Hummingbirds](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a8d585f-99dd-4e5d-b593-c7eaddfe8ce4%2Fe474366a-506b-4a64-a253-3e34eb51e3d2%2F0rh4d76_processed.png&w=3840&q=75)
Transcribed Image Text:**Allen’s Hummingbird Study**
Allen's hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther. A small group of 20 Allen's hummingbirds in Arizona was observed. The average weight for these birds is \(\bar{x} = 3.15\) grams. Previous studies suggest that the weights of Allen's hummingbirds follow a normal distribution, with \(\sigma = 0.32\) gram.
**(a) 80% Confidence Interval Calculation**
Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. Determine the margin of error. (Round answers to two decimal places.)
- Lower limit: [ ]
- Upper limit: [ ]
- Margin of error: [ ]
**(b) Necessary Conditions**
Select all necessary conditions for your calculations:
- [ ] Normal distribution of weights
- [ ] \(\sigma\) is known
- [ ] \(n\) is large
- [ ] \(\sigma\) is unknown
- [ ] Uniform distribution of weights
**(c) Interpretation of Results**
Interpret the results in the context of this problem:
- ( ) 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.
- ( ) 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) Sample Size for 80% Confidence with Maximum Margin of Error**
Find the sample size necessary for an 80% confidence level with a maximal margin of error \(E = 0.16\) for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
- [ ] Hummingbirds
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