Answered: Find a 95% confidence interval for the…

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

Many cardiac patients wear an implanted pacemaker to control their
heartbeat. A plastic connector module mounts on the top of the
pacemaker. A random sample of 75 modules has an average depth of
0.310 inch. Assuming a standard deviation of 0.0015 inch and an
approximately normal distribution.

a.) Find a 95% confidence interval for the mean of the depths of all
connector modules made by a certain manufacturing company.
b.) How large a sample is needed if we wish to be 95% confident that our
sample mean will be within 0.0005 inch of the true mean?

Ans:

A.0.3097 in < u < 0.3103 in
B. 35

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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