Answered: A confidence interval is desired for…

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 confidence interval is desired for the true mean stray-load loss (Watts) for a certain type of induction motor. Assume that the stray-load loss is normally distributed with =3.3Watts.

Situation 3: You take 100 measurements of stray-load loss from induction motors and determine that the mean of your sample is 53.6 Watts. When you calculate the 95% confidence interval for this situation, you get: (52.95 Watts, 54.25 Watts) is a 95% confidence interval for M.

Compare this confidence interval to the interval you calculated in Situation 1. They are both 95% confidence intervals, but they have different sample sizes. What effect did sample size have on the interval estimate endpoints?

Question 1: 25 sample size, Confidence Interval: (52.3064,54.8936)

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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