MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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
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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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