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A particular brand of cereal advertises it packages weigh 510 g. You wish to determine if on the average the weight is less than 510g. A simple random sample of 81 packages from a large lot are weighed. The average weight is found to be 509.5 g with a standard deviation of 0.4 g. 1. Perform a test at a level of significance 0.05. 2. What is the power of the test if you wish to detect an average departure of 0.2 g underweight (can be stated as weighing 509.8g).  3. What sample size is needed to have a power of 90%?  Please show all steps. Thank you!

A particular brand of cereal advertises it packages weigh 510 g. You wish to determine if on the average the weight is less than 510g. A simple random sample of 81 packages from a large lot are weighed. The average weight is found to be 509.5 g with a standard deviation of 0.4 g. 1. Perform a test at a level of significance 0.05. 2. What is the power of the test if you wish to detect an average departure of 0.2 g underweight (can be stated as weighing 509.8g).  3. What sample size is needed to have a power of 90%?  Please show all steps. Thank you!

MATLAB: An Introduction with Applications
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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A particular brand of cereal advertises it packages weigh 510 g.
You wish to determine if on the average the weight is less than 510g. A simple random
sample of 81 packages from a large lot are weighed. The average weight is found to be
509.5 g with a standard deviation of 0.4 g.

1. Perform a test at a level of significance 0.05.

2. What is the power of the test if you wish to detect an average departure of 0.2 g
underweight (can be stated as weighing 509.8g). 

3. What sample size is needed to have a power of 90%? 

Please show all steps. Thank you!

Expert Solution
Step 1

Given a particular brand of cereal advertises the weight will be 510 g

μ = 510 g

n = 81x¯=509.5 gσ = 0.4 g

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