Answered: A random sample of 70 observations from…

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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Question

A random sample of 70 observations from a normally distributed population possesses a sample mean
equal to 26.2 and a sample standard deviation equal to 4.1.
a. Calculate an approximate 95% confidence interval for ?.
b. What do you mean when you say that a confidence coefficient is 0.95?
c. Calculate an approximate 99% confidence interval for ?.
d. What happens to the width of a confidence interval as the confidence level is increased (all else constant)?
What is the tradeoff between the confidence level and the precision of the estimate? Explain.
e. Would your confidence intervals of parts a and c be valid if the distribution of the original population was
not normal?

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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