Answered: A certain brand produces milk with…

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

A certain brand produces milk with boxes in weight of 85 gr. The average weight of 11 samples equals 85.42 gr. Assume that the distribution of the weight of the product is 1.24. Conduct a test about the standard weight of the milk boxes. Does the product still weigh 85 gr or higher? Write down the z value which you should use for comparison. (Use at least 2 digits after decimal: sensitivity: 0.00)

Expert Solution

Step 1

The null and alternative hypothesis are given as :

$H_{0} : μ = 85 g r H_{1} : μ > 85 g r$

The sample mean and population standard deviation are $85.42 g r a n d 1.24$ .

The test statistics is given by :

$z = \frac{x - μ}{σ / \sqrt{n}} ~ N (0, 1)$

$\begin{array}{rcl} z & = & \frac{85.42 - 85}{1.24 / \sqrt{11}} \\ z & = & 1.12 \end{array}$

Let the level of significance be $α = 0.05$

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