Answered: Quantitative Methods 1 QUESTION 5a -…

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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Quantitative Methods 1

QUESTION 5a - problem-type question requiring detailed written answers.

A machine packages sugar in bags which have a mean weight of 250grams and standard deviation of 5 grams. The machine was recently serviced and it is believed that the mean weight of the bags has changed but the standard deviation has remained the same. A random sample of 45 bags gave a mean of 248.4 grams. Test at a 2% level of significance whether the mean weight of the bags is different from 250 grams.

i) State the null and alternative hypotheses for this test.

ii) Find the p-value for the test of hypothesis.

iii) Will the null hypothesis be rejected at a 2% significance level?

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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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