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An experiment measures the distribution of a variable in 5 bins. The established theory predicts for this measurement a linear decrease with the bin number: bin 1 2 3 4 5 prediction 32 28 24 22 18 The experiment measures the following number of events: bin 1 2 3 45 21 14 8 observed events: 36 26 a) Formulate the null-hypothesis Ho. b) Perform a x2 test and comment on the outcome. c) Now derive the p-value and state whether the theory is excluded at the 30 significance level. State the probability for a type-1 error. d) The experiment realizes that their measured numbers per bin are affected by a Gaussian systematic uncertainty of σsys = 3.5. This uncertainty is not correlated across the bins. Perform the necessary calculations and derive an updated statement about whether the theory is excluded at a significance of 30. Suggest a way to improve the sensitivity of the measurement.

An experiment measures the distribution of a variable in 5 bins. The established theory predicts for this measurement a linear decrease with the bin number: bin 1 2 3 4 5 prediction 32 28 24 22 18 The experiment measures the following number of events: bin 1 2 3 45 21 14 8 observed events: 36 26 a) Formulate the null-hypothesis Ho. b) Perform a x2 test and comment on the outcome. c) Now derive the p-value and state whether the theory is excluded at the 30 significance level. State the probability for a type-1 error. d) The experiment realizes that their measured numbers per bin are affected by a Gaussian systematic uncertainty of σsys = 3.5. This uncertainty is not correlated across the bins. Perform the necessary calculations and derive an updated statement about whether the theory is excluded at a significance of 30. Suggest a way to improve the sensitivity of the measurement.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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An experiment measures the distribution of a variable in 5 bins. The established theory predicts for this measurement a linear decrease with the bin number: bin 1 2 3 4 5 prediction 32 28 24 22 18 The experiment measures the following number of events: bin 1 2 3 45 21 14 8 observed events: 36 26 a) Formulate the null-hypothesis Ho.
Transcribed Image Text:An experiment measures the distribution of a variable in 5 bins. The established theory predicts for this measurement a linear decrease with the bin number: bin 1 2 3 4 5 prediction 32 28 24 22 18 The experiment measures the following number of events: bin 1 2 3 45 21 14 8 observed events: 36 26 a) Formulate the null-hypothesis Ho.
b) Perform a x2 test and comment on the outcome. c) Now derive the p-value and state whether the theory is excluded at the 30 significance level. State the probability for a type-1 error. d) The experiment realizes that their measured numbers per bin are affected by a Gaussian systematic uncertainty of σsys = 3.5. This uncertainty is not correlated across the bins. Perform the necessary calculations and derive an updated statement about whether the theory is excluded at a significance of 30. Suggest a way to improve the sensitivity of the measurement.
Transcribed Image Text:b) Perform a x2 test and comment on the outcome. c) Now derive the p-value and state whether the theory is excluded at the 30 significance level. State the probability for a type-1 error. d) The experiment realizes that their measured numbers per bin are affected by a Gaussian systematic uncertainty of σsys = 3.5. This uncertainty is not correlated across the bins. Perform the necessary calculations and derive an updated statement about whether the theory is excluded at a significance of 30. Suggest a way to improve the sensitivity of the measurement.
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