# CU-Boulder MCEN 3037 - 17R (14 pages)

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## 17R

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- Pages:
- 14
- School:
- University of Colorado at Boulder
- Course:
- Mcen 3037 - Data Analysis

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Measures plausibility of null hypothesis through P value What is the correct P value below which we reject H0 From a practical standpoint we really want a firm cutoff Why Here we may define a cutoff point for the P value fixed level test Choose a value for a If P a 0 a 1 Significance level Null hypothesis rejected Alternate hypothesis taken as truth Common choice a 0 05 Critical point value of test statistic that produces P a dividing line for test statistic One side H0 rejected rejection region Other side H0 not rejected Let s look at an example A new concrete mix is being evaluated The plan is to sample 100 blocks made with the new mix compute the sample mean compressive strength and then test H 0 1350 MPa H1 1350 MPa We assume from other similar tests that the sample standard deviation is 70 MPa Find the critical point and the rejection region if the test will be conducted at a significance level of 5 We need to find the critical point x x We have P 0 05 S x 70 N 100 What is our test statistic Critical value Rejection region z 1 65 H 0 1350 MPa H1 1350 MPa Rejection region x z Sx N x 1350 1 65 7 x 1361 55 P 0 05 S x 70 N 100 Determine x x z Sx N x 1350 1 65 7 x 1361 55 Type I and Type II Errors Fixed level testing results in a firm decision In what way can we be wrong H 0 1350 MPa H1 1350 MPa We reject H0 when in fact it is TRUE TYPE I error We fail to reject H0 when in fact it is FALSE TYPE II error For a successful experimental plan we want to make the probability of having type I and type II errors small We can now look at the probabilities of each type of error TYPE I error We reject H0 when in fact it is TRUE Let s use H 0 1350 MPa a 0 05 H1 1350 MPa Mean lies in here x Probability of a type I always less than or equal to a Rejection region TYPE II error We fail to reject H0 when in fact it is FALSE To do this we compute the POWER of a test Power 1 P type II We want Power to be large Why H 0 1350 MPa H1 1350 MPa If the power is large the probability of a

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