A machine fills 'one litre' water bottles. When the machine is working correctly the contents of the bottles are normally distributed with mean 1.002 litres and standard deviation 0.002 litres. The performance of the machine is tested at regular intervais by taking a sample of 9 bottles and calculating their mean content. If this mean content falls below a certain value, it is assumed that the machine is not performing correctly and it is stopped. (a) Set up null and altemative bypotheses for a test of whether the machine is working correctly. (b) For a test at the 5% significance level, find the rejection region taking the sample mean as the test statistic. (G) Giy the value for the probability of a Type I error.
A machine fills 'one litre' water bottles. When the machine is working correctly the contents of the bottles are normally distributed with mean 1.002 litres and standard deviation 0.002 litres. The performance of the machine is tested at regular intervais by taking a sample of 9 bottles and calculating their mean content. If this mean content falls below a certain value, it is assumed that the machine is not performing correctly and it is stopped. (a) Set up null and altemative bypotheses for a test of whether the machine is working correctly. (b) For a test at the 5% significance level, find the rejection region taking the sample mean as the test statistic. (G) Giy the value for the probability of a Type I error.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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This is an A level Mathematics question. It is on Type of Errors from Hypothesis Testing.
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
Transcribed Image Text:A machine fills "one litre' water bottles. When the machine is working correctly the contents
of the bottles are normally distributed with mean 1.002 litres and standard deviation
0.002 litres. The performance of the machine is tested at regular intervals by taking a sample
of 9 bottles and calculating their mean content. If this mean content falls below a certain
value, it is assumed that the machine is not performing correctly and it is stopped.
(a) Set up null and altemative hypotheses for a test of whether the machine is working
correctly.
(b) For a test at the 5% significance level, find the rejection region taking the sample
mean as the test statistic,
(c) Give the value for the probability of a Type I error.
(d) Find P(Type II error) if the mean content of the bottles has fallen to the nominal
value of 1.000 litre.
(e) Find the range of values of u for which the probability of making a Type II error is
less than 0.001.
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