Student Activity : Point Estimates ( Mean and Standard Deviation) Directions: Study the following problem and do the indicated tasks to provide the missing information in the solution. Problem: Mr. Domingo conducted a survey among ten random samples of people who are in favor of Truck Ban in a section in the City. He determined the percentages of those who are in favor of the ban. Assuming that the only error present is the sampling error, he wanted to determine the point estimate of the population mean percentage and the standard deviation based on 500 observations. The following numbers represent the percentages of the 10 surveys. 47.0 56.4 50.1 60.2 48.0 55.3 60.0 59.5 63.0 57.5 Solution: STEPS SOLUTION 1. Find the mean of the percentages. Formula: x=∑Xn,whereXisapercentagex=∑Xn,whereXisapercentage x=47.0+56.4+50.1+...+57.510x=47.0+56.4+50.1+...+57.510= 2. Give the estimate of the population mean percentage. The estimate of the population mean percentage is . Compute the standard deviation. STEPS SOLUTION 1. Find the sum of the values in the numerator and n-1. S^2=(∑(X-x ̅ )^2)/(n-1) S^2=((47.0-55.7)^2+(56.4-〖55.7)〗^2+...+(57.5-〖55.7)〗^2)/(10-1) s2= This value is called the _________ 2. Extract the square root of s2 s= _ This value is called the ______. 3. Describe/Interpret the result. On the average, the sample mean percentage is away from the mean of the percentage value of people favoring the truck ban.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Student Activity : Point Estimates ( Mean and Standard Deviation)

Directions: Study the following problem and do the indicated tasks to provide the missing information in the solution.

Problem:

Mr. Domingo conducted a survey among ten random samples of people who are in favor of Truck Ban in a section in the City. He determined the percentages of those who are in favor of the ban. Assuming that the only error present is the sampling error, he wanted to determine the point estimate of the population mean percentage and the standard deviation based on 500 observations. The following numbers represent the percentages of the 10 surveys.

47.0

56.4

50.1

60.2

48.0

55.3

60.0

59.5

63.0

57.5

Solution:

STEPS

SOLUTION

1. Find the mean of the percentages.

Formula: x=∑Xn,whereXisapercentagex=∑Xn,whereXisapercentage

x=47.0+56.4+50.1+...+57.510x=47.0+56.4+50.1+...+57.510= __________

2. Give the estimate of the population mean percentage.

The estimate of the population mean percentage is ________________.

Compute the standard deviation.

STEPS	SOLUTION
1. Find the sum of the values in the numerator and n-1.	S^2=(∑(X-x ̅ )^2)/(n-1) S^2=((47.0-55.7)^2+(56.4-〖55.7)〗^2+...+(57.5-〖55.7)〗^2)/(10-1) s2=__________ This value is called the _______________________
2. Extract the square root of s²	s= _____________ This value is called the ______________________.
3. Describe/Interpret the result.	On the average, the sample mean percentage is __________ away from the mean of the percentage value of people favoring the truck ban.

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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