Hypothesis Tests and Chi-Squared Tests in Statistics and Reliability of Systems

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[...] by the table and we add the totals: Dysfunction 1 Type 2 Type 3 Type 4 Total Assemblage 1 Assemblage 2 Total Then we get an indicator of . The degree of freedom is worth In the table the theoretical value of for a threshold of significance of (pour ) est . On a so this means we reject the independence between types of malfunction and assembly techniques. Therefore, we can assert (with with a chance of making a mistake) that there is a dependence between types of malfunction and assembly techniques. [...]

[...] The mean of the sample is given by and its standard deviation is where is the size of the sample and the are here the masses of the pieces. Supplier A : and Supplier B : and We are in the case of a test for comparison of observed means with unknown standard deviations and large samples" . We calculate the quantity: . At the error threshold the hypothesis according to which the means of the masses are the same for the two suppliers is rejected if with . [...]

[...] The percentage of sick days and work accidents in relation to the number of working days is: - for the 1st stream - for the 2nd stream 2. We are in the case of a test for comparing two observed proportions. We calculate the quantity with and . and . On a ; ; ; so the application conditions are well met. Then we have . At the level of confidence of (so error threshold of the hypothesis according to which the proportions are the same for both fields is rejected if with . [...]

[...] We can therefore accept the hypothesis according to which the difference in proportions is not simply due to a statistical fluctuation. Exercise n°5 We start by calculating the average and the standard deviation from the sample: and . We then calculate the average and the standard deviation theoretical by the same calculation method: and . We are in the case of a test for comparison of means with unknown population standard deviations and large samples . We calculate the quantity: . [...]

[...] Statistics and Reliability of Systems - Hypothesis Tests and Chi-Squared Tests Exercise 1 On a . On a small sample of 23 cafes, a random variable following a normal law and a standard deviation unknown At the error threshold the hypothesis according to which the mean is equal to the observed expectation is rejected " . On a so the hypothesis is not rejected. We can therefore validate the expectation on the actual content of coffee poured. Exercise n°2 1. [...]