# CU-Boulder MCEN 3037 - 16R (14 pages)

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## 16R

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

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Tests for a population proportion What is a population proportion No more than 10 of people in Colorado thought that the Colts would beat the Broncos Mean of a bunch of 0 s and 1 s 0 won t beat them 1 will be them The probability of success p 0 10 Is this claim true What are the mean and variance of a Bernoulli trial p 0 10 2 p 1 p From the central limit theorem proportions drawn from the population will have a normal distribution p 0 10 n p 1 p 0 3 n n Ok say we sample 400 fans and get 12 5 thinking that the colts will win H 0 10 How can we test our original claim H1 10 Let s calculate the z value 0 125 0 10 z 1 666 0 3 400 What is the P value 0 0475 What do we conclude Here this is close it is just below 0 05 and may be sufficient to reject the null hypothesis Let s try an example Spacer collars for a transmission countershaft have a thickness specification of 38 98 39 02 mm The process that manufactures the collars is supposed to be calibrated to give a mean thickness of 39 mm A sample of 6 collars is drawn and measured for thickness giving 39 030 38 997 39 012 39 008 39 019 and 39 002 Can you conclude that the process needs recalibration What do we do What hypothesis do we want to test H 0 39 H1 39 We have a small sample size so let s use the t statistic From our sample we have What is the t value t 5 x 39 0113 S x 0 011928 39 00113 39 2 327 0 011928 6 This is a 2 sided Hypothesis Test What is the P value t 5 2 327 What is the P value It looks like it s between 0 05 and 0 10 Should we recalibrate We may want to recalibrate We do not have sufficient evidence to reject the null hypothesis but we re also not too confident that it is in calibration It s best to consider an example We re worried that ambient temperature may have an effect on out manufacturing process for ball bearings Morning cool we sample 120 ball bearings x 5 068mm S x 0 011mm Afternoon hot we sample 65 ball bearings y 5 072mm S y 0 007mm Can we conclude that the bearings in the morning have

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