A simple random sample of size n is drawn from a population that is normally distributed. The sample mean,x,is found to be112,and the sample standard deviation, s, is found to be10.(a) Constructan80%confidence interval aboutμif the sample size, n, is24.(b) Constructan80%confidence interval aboutμif the sample size, n, is15.(c) Constructa70%confidence interval aboutμif the sample size, n, is24.(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?

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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 simple random sample of size n is drawn from a population that is normally distributed. The sample mean,

is found to be

112,

and the sample standard deviation, s, is found to be

10.

(a) Construct

80%

confidence interval about

if the sample size, n, is

24.

(b) Construct

80%

confidence interval about

if the sample size, n, is

15.

70%

confidence interval about

if the sample size, n, is

24.

(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?

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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