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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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