# CU-Boulder MCEN 3037 - 14R (15 pages)

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## 14R

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## 14R

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Mcen 3037 - Data Analysis
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We need to accept or reject a statement about some parameter of a population Statement is called the Hypothesis Random variable Example We are interested in the burn rate of a solid rocket propellant We may be interested in determining if the mean burn rate is 50 cm s Null hypothesis we want to test H 0 50 We say H1 50 Alternative hypothesis rejecting null hypothesis leads to accepting alternative hypothesis How do we determine the value of the population parameter specified by the null hypothesis Past experience Theory Evaluation want to know if engineering design specifications were met Hypothesis testing relies on information from a random sample If this is consistent with the null hypothesis then we conclude it is plausible If not then we conclude it is false Reject H 0 50 How does our sample mean compare with 50 H 50 1 A certain type of car engine emits a mean of 100 mg s of oxides of nitrogen NOx at 100 horsepower A modification to the engine has been proposed that may reduce NOx emissions and it will be put into production if the emission is less than 100 mg s A sample of 50 modified engines are built and tested that have a mean NOx emission of 92 mg s and a standard deviation of 21mg s What are the possible interpretations of this result 1 Population mean is actually greater than 100 sample mean is lower due to random variations Null hypothesis 2 Population mean is actually less than 100 experimental data is real alternative hypothesis A certain type of car engine emits a mean of 100 mg s of oxides of nitrogen NOx at 100 horsepower A modification to the engine has been proposed that may reduce NOx emissions and it will be put into production if the emission is less than 100mg A sample of 50 modified engines are built and tested that have a mean NOx emission of 92 mg s and a standard deviation of 21mg s Hypothesis Testing put the null hypothesis on trial H 0 100 H1 100 Hypothesis test measure the strength of disagreement between the sample and Ho to produce

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