Fundamentals of Statistics (5th Edition)

5th Edition

ISBN: 9780134508306

Author: Michael Sullivan III

Publisher: PEARSON

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Chapter B.2, Problem 10AYU

A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample variance, s², is determined to be 19.8.

(a) Construct a 95% confidence interval for σ² if the sample size, n, is 10.
(b) Construct a 95% confidence interval for σ² if the sample size, n, is 25. How does increasing the sample size affect the width of the interval?
(c) Construct a 99% confidence interval for σ² if the sample size, n, is 10. Compare the results with those obtained in part (a). How does increasing the level of confidence affect the width of the confidence interval?

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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Chapter B.2, Problem 9AYU

Chapter B.2, Problem 11AYU

Chapter B.2 Solutions

Fundamentals of Statistics (5th Edition)

Ch. B.2 - True or False: The chi-square distribution is...Ch. B.2 - Prob. 2AYU Ch. B.2 - Prob. 3AYU Ch. B.2 - Prob. 4AYU Ch. B.2 - Prob. 5AYU Ch. B.2 - Prob. 6AYU Ch. B.2 - In Problems 58, find the critical values 1/22 and...Ch. B.2 - Prob. 8AYU Ch. B.2 - Prob. 9AYU Ch. B.2 - A simple random sample of size n is drawn from a...

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Solution Summary: The author explains the 95% confidence interval for sigma2 for a random sample of size n, which follows chi-square distribution with degrees of freedom.

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Chapter B.2 Solutions