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Name: According to a packaging, a box should weigh 720 grams. One person sus
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Description: According to a packaging, a box should weigh 720 grams. One person suspects that the boxes weigh too little and then made an attempt and bought 12 number of boxes. Each box was weighed and the mean value of the boxes was calculated as 715.4 gram. 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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According to a packaging, a box should weigh 720 grams. One person suspects that the boxes weigh too little and then made an attempt and bought 12 number of boxes. Each box was weighed and the mean value of the boxes was calculated as 715.4 gram. The weight is assumed to be normally distributed with a known standard deviation of 10 grams.

(i) Perform a hypothesis test to test the suspicion that the boxes weigh too little. Set up the hypothesis to investigate the suspicion, perform the test at the significance level 0.05. Based on the result of the test, is the person right in his suspicions?

(ii) What is the strength of the test in a) when = 710 grams?

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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