Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 18 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 ? = 0.24 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.) a. ? is known b. normal distribution of weights c. n is large d. uniform distribution of weights e. ? is unknown (c) Interpret your results in the context of this problem. a. We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval. b. We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval. c. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80. d. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20. (d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.07 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

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 (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 18 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 ? = 0.24 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.)

a. ? is known

b. normal distribution of weights

c. n is large

d. uniform distribution of weights

e. ? is unknown

a. We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval.

b. We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval.

c. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

d. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.07 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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