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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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A government report says that the average amount of money spent per U.S. household per week on food is about $30. A random sample of 50 households in a small city is selected, and their weekly spending on food is recorded. The Minitab output below shows the results of data for the population mean μ. (a ) Determine whether there are any outliers (b) Explain why the Normal condition is met in this case. (c)Carry out a signigicance test H0: μ =30 and Ha: μ ≠ 30 at 0.05 significance level

Variable
N
Mean
SE Mean
StDev
Minimum
Q1
Median
Q3
Maximum
Weight (oz) 50
31.935
0.339
2.394
26.491 29.990 31.739 34.115
35.547

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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