Answered: How many users must be included in 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

How many users must be included in the sample if you want to be 95% confident that the sample mean is within 10 users of the population mean? Compare your answer with Example #6 (in the picture).

Identify z_c, E, and s.
Use z_c, E, and sd ≈ s to find the minimum sample size n.
Interpret the results and compare with exampl #6 (in the picture)

EXAMPLE #6
Problem: You want to estimate the mean
number of friends for all users of the website.
How many users must be included in the
sample if you want to be 95% confident that
the sample mean is within seven friends of
the population mean?
EXAMPLE #6
Solution: Using c = 0.95, z = 1.96, o s≈ 53.0 (from
Example #2), and E = 7, you can solve for the minimum
sample size n. n = = (²0)² = (1⁹6-53.0) ² ≈ 220.23.
E
7
When necessary, round up to obtain a whole number. So,
you should include at least 221 users in your sample.
Interpretation: You already have 40, so you need 181
more. Note that 221 is the minimum number of users to
include in the sample. You could include more, if desired.

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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