Construct a 95% confidence interval for the mean number of friends for all users of the website. Compare your result with the interval found in Example #3 (given in the photo).a. Find x̅ and E.b. Find the left and right endpoints of the confidence interval.c. Interpret the results and compare them with Example #3. EXAMPLE #3Problem: Use the data given in Example #1 to construct a 95% confidence intervalfor the mean number of friends for all users of the website.Solution: In Examples #1 and #2, you found that x = 130.8 and E≈ 16.4. Theconfidence interval is as follows.Left EndpointRight Endpointx - E ~ 130.8 – 16.4 = 114.4 x+E 130.8 + 16.4 = 147.2114.4114.4 << 147.2130.8147.2110 115 120 125 130 135 140 145 150XInterpretation: With 95% confidence, you can say that the population mean numberof friends is between 114.4 and 147.2.32 Sample DataNumber of Friends162 114 131 87 10863249 135 172 196 127 100146 21480 557113095 156 201227 137125145 17974 215 137 124

Answered: Problem: Use the data given in Example…

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

Construct a 95% confidence interval for the mean number of friends for all users of the website. Compare your result with the interval found in Example #3 (given in the photo).

a. Find x̅ and E.
b. Find the left and right endpoints of the confidence interval.
c. Interpret the results and compare them with Example #3.

EXAMPLE #3
Problem: Use the data given in Example #1 to construct a 95% confidence interval
for the mean number of friends for all users of the website.
Solution: In Examples #1 and #2, you found that x = 130.8 and E≈ 16.4. The
confidence interval is as follows.
Left Endpoint
Right Endpoint
x - E ~ 130.8 – 16.4 = 114.4 x+E 130.8 + 16.4 = 147.2
114.4
114.4 << 147.2
130.8
147.2
110 115 120 125 130 135 140 145 150
X
Interpretation: With 95% confidence, you can say that the population mean number
of friends is between 114.4 and 147.2.
32

Sample Data
Number of Friends
162 114 131 87 108
63
249 135 172 196 127 100
146 214
80 55
71
130
95 156 201
227 137
125
145 179
74 215 137 124

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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