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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 or = 0.30 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 is known uniform distribution of weights n is large normal distribution of weights o is unknown (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 0.80. 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 0.20.

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 or = 0.30 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 is known uniform distribution of weights n is large normal distribution of weights o is unknown (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 0.80. 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 0.20.

MATLAB: An Introduction with Applications
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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**Educational Text on Confidence Intervals for Allen's Hummingbird Weight Study** --- **Background Information:** Allen's hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther. In a study conducted in Arizona, a sample of 14 birds was examined. The average weight for these birds is recorded as \( \overline{x} = 3.15 \) grams. Previous studies suggest the weights of Allen's hummingbirds follow a normal distribution with a standard deviation \( \sigma = 0.30 \) gram. **Analysis:** **(a) Confidence Interval Calculation:** - Task: Find an 80% confidence interval for the average weight of Allen's hummingbirds in the study region. Calculate the margin of error and provide the lower and upper limits rounded to two decimal places. **(b) Necessary Conditions for Calculation:** - Considerations: - **\( \sigma \) is known** - **Uniform distribution of weights** - **Sample size \( n \) is large** - **Normal distribution of weights** - **\( \sigma \) is unknown** **(c) Interpretation of Results:** - Statements to Consider: - 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 0.80. - 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 0.20. **(d) Sample Size Determination:** - Task: Determine the necessary sample size for an 80% confidence level with a maximal margin of error \( E = 0.08 \) for the mean weights of the hummingbirds. Round up to the nearest whole number. --- This exercise is designed to deepen your understanding of statistical concepts like confidence intervals, margin of error, and sample size determination through a practical study of hummingbird weights.
Transcribed Image Text:**Educational Text on Confidence Intervals for Allen's Hummingbird Weight Study** --- **Background Information:** Allen's hummingbird (*Selasphorus sasin*) has been studied by zoologist Bill Alther. In a study conducted in Arizona, a sample of 14 birds was examined. The average weight for these birds is recorded as \( \overline{x} = 3.15 \) grams. Previous studies suggest the weights of Allen's hummingbirds follow a normal distribution with a standard deviation \( \sigma = 0.30 \) gram. **Analysis:** **(a) Confidence Interval Calculation:** - Task: Find an 80% confidence interval for the average weight of Allen's hummingbirds in the study region. Calculate the margin of error and provide the lower and upper limits rounded to two decimal places. **(b) Necessary Conditions for Calculation:** - Considerations: - **\( \sigma \) is known** - **Uniform distribution of weights** - **Sample size \( n \) is large** - **Normal distribution of weights** - **\( \sigma \) is unknown** **(c) Interpretation of Results:** - Statements to Consider: - 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 0.80. - 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 0.20. **(d) Sample Size Determination:** - Task: Determine the necessary sample size for an 80% confidence level with a maximal margin of error \( E = 0.08 \) for the mean weights of the hummingbirds. Round up to the nearest whole number. --- This exercise is designed to deepen your understanding of statistical concepts like confidence intervals, margin of error, and sample size determination through a practical study of hummingbird weights.
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