**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.

Method: Use z statistic to find the confidence interval and margin of error

Answered: Allen's hummingbird (Selasphorus sasin)…

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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