Answered: You would like to construct a 99%…

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

You would like to construct a

99%

confidence interval to estimate the population mean score on a nationwide examination in finance, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of

492

and a standard deviation of

(a) What is the best point estimate, based on the sample, to use for the population mean?

(b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the

99%

confidence interval for the population mean.

(In the table, Z refers to a standard normal distribution, and

refers to a t distribution.)

Sampling scenario	Z	t	Could use either Z or t	Unclear
The sample has size 17 , and it is from a population with a distribution about which we know very little.			Z t
The sample has size 20 , and it is from a normally distributed population with an unknown standard deviation.			Z t
The sample has size 100 , and it is from a non-normally distributed population with a known standard deviation of 77 .			Z t

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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