A biology student measured the ear lengths of an SRS of 10 Mountain cottontail rabbits. The ear lengths are listed in the table attached image:Suppose that the distribution of ear lengths of all Mountain cottontail rabbits follows a Normal distribution with a standard deviation of 0.4 cm.(a) By hand, calculate a 95% confidence interval for the mean ear length of Mountain cottontail rabbits.(b) Re-calculate the above interval, using R.(c) By hand, calculate a 99% confidence interval for the mean ear length of Mountain cottontail rabbits.(d) Your friend says that the interval in part (c) can be interpreted as:“The probability is 99% that the mean ear length of all Mountain cottontail rabbits is in the interval we obtained in part (c).”Explain why this interpretation is not correct, and give the correct interpretation of the “99% confidence.” Rabbit #1Ear length (cm) 5.425.536.04565.6 4.9 5.075.185.996.2105.5

Given: Sample size n=10 Population standard deviation σ=0.4

Answered: A biology student measured the ear…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 10CR

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A biology student measured the ear lengths of an SRS of 10 Mountain cottontail rabbits. The ear lengths are listed in the table attached image:

Suppose that the distribution of ear lengths of all Mountain cottontail rabbits follows a Normal distribution with a standard deviation of 0.4 cm.

(a) By hand, calculate a 95% confidence interval for the mean ear length of Mountain cottontail rabbits.

(b) Re-calculate the above interval, using R.

(d) Your friend says that the interval in part (c) can be interpreted as:

“The probability is 99% that the mean ear length of all Mountain cottontail rabbits is in the interval we obtained in part (c).”

Explain why this interpretation is not correct, and give the correct interpretation of the “99% confidence.”

Rabbit #
1
Ear length (cm) 5.4
2
5.5
3
6.0
4
5
6
5.6 4.9 5.0
7
5.1
8
5.9
9
6.2
10
5.5

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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