# CU-Boulder MCEN 3037 - 23 (27 pages)

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Mcen 3037 - Data Analysis
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Exam 2 Thursday Correlation and Linear regression Hypothesis Testing Fourier Transforms Linear Systems 0th and 1st order Hypothesis Testing Small and large sample Relation to confidence intervals Population proportions Difference between 2 means Type 1 and Type II errors Level Testing and Power Equations Given General first order system dt y KF t dy Solution for sine input y t ce t KA 1 2 2 sin t arctan Euler Formulas 1 a0 T T 2 T 2 f t dt an 2 T T 2 T 2 f t cos n 2 t dt T bn 2 T Tables correlation coefficient t table z table T 2 T 2 f t sin n 2 t dt T In a sample of 150 households in a certain city 110 had high speed internet access Can you conclude that more than 70 of the households in this city have high speed internet access H 0 0 7 H 1 0 7 Variance p 1 p 0 7 0 3 0 21 Standard Deviation 0 21 0 4582 Your Sample Gave 110 0 7333 150 0 7333 0 7 z 0 89 0 4582 150 0 7333 0 7 z 0 89 0 4582 150 We get a P value of 0 1867 SO We can t conclude that more than 70 have access Example Shipments of nuts are checked for moisture content Five moisture measurements will be made on nuts chosen at random from the shipment Moisture content is reported in percent per weight the true moisture content is 12 and the standard deviation is 1 5 H 0 10 You are interested in testing the hypothesis at the 5 level H1 10 What is the power of the test Find the critical point x 10 2 132 1 5 5 x 11 43 t4 0 45 x 10 2 132 1 5 5 x 11 43 t4 0 45 11 43 12 12 11 43 0 849 1 5 5 P 0 55 t4 P P 0 275 2 The power is 0 5 0 275 0 775 Unchanged by multiplying each value of a variable by a constant Unchanged by adding a constant to each variable Unchanged by interchanging x and y For a given sample size we need to determine whether a given rxy is significant or a result of pure chance For practical problems we can consult a table General procedure Calculate rxy from the measured data Determine level of significance a required a gives the probability that an experimental value of rxy will be greater by pure

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