A machine fills "one litre' water bottles. When the machine is working correctly the contentsof the bottles are normally distributed with mean 1.002 litres and standard deviation0.002 litres. The performance of the machine is tested at regular intervals by taking a sampleof 9 bottles and calculating their mean content. If this mean content falls below a certainvalue, 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 workingcorrectly.(b) For a test at the 5% significance level, find the rejection region taking the samplemean 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 nominalvalue of 1.000 litre.(e) Find the range of values of u for which the probability of making a Type II error isless than 0.001.

Name: A machine fills "one litre' water bottles. When the machine is workin
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Description: A machine fills "one litre' water bottles. When the machine is working correctly the contentsof the bottles are normally distributed with mean 1.002 litres and standard deviation0.002 litres. The performance of the machine is tested at regular inter

mean = 1.002 standard deviation = 0.002 n=9

Math

Statistics

(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. (c) Give the value for the probability of a Type I error.

(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. (c) Give 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

Section: Chapter Questions

Problem 1P

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