An experiment was performed in a New Mexico recreational vehicle on a chemical manufacturing process by making 50 batches of N-methylamphetamine using a standard production method (A) followed by 50 batches using a modified method (B). Method A yield: 108.4, 73.7, 86.7, 69.6, 87, 81.5, 103.9, 460, 86, 84.7, 111.1, 83.3, 78.2, 83, 85.7, 97.6, 84.2, 81.5, 83.9, 85.8, 82, 92.5, 85.3, 86.4, 85.4, 80.3, 84.5, 87.4, 19.7, 83.4, 103.9, 82.8, 85.6, 81.2, 85.6, 82.3, 84.9, 90.6, 56.3, 83, 11.6, 121, 87.2, 85.4, 80.6, 84.1, 86.3, 66.7, 83, 85.1 Method B yield: 87.2, 82.6, 88.3, 86.6, 85.1, 80.7, 87, 85.6, 89.8, 89.8, 85.2, 85.6, 89.2, 89.8, 85.2, 84.5, 87.4, 88, 83.9, 86.1, 86.3, 82, 81.7, 87.3, 84.8, 91.2, 81.7, 87.7, 86.7, 82.4, 88.2, 86.4, 87.1, 84.6, 87.4, 89.2, 83, 83.2, 87, 85.5, 85.5, 85.6, 86.1, 89, 90.1, 84.5, 89.2, 87.5, 88.5, 89.0 a. What is the (MLE) average yield for method A

The MLE average yield for method A is 61.22.The MLE is calculated by finding the value of the parameter that maximizes the likelihood function.

The MLE (maximum likelihood estimate) average yield for method A can be calculated by taking the sum of all the yields for method A (excluding outliers) and dividing by the number of batches (n=48). Outliers can be identified using box plots or statistical tests.

Sum of yields for method A = 2938.7

MLE average yield for method A = 2938.7/48 = 61.22 (rounded to two decimal places)

MLE stands for maximum likelihood estimate, which is a statistical method used to estimate the parameters of a statistical model. In this case, the MLE average yield for method A is the maximum likelihood estimate of the true average yield for the standard production method used in the experiment.

In this case, the parameter of interest is the true average yield for method A, and the likelihood function is a probability distribution that describes the distribution of yields observed in the 50 batches produced using method A. The MLE average yield for method A is therefore the value of the true average yield that maximizes the likelihood of obtaining the observed yields for the 50 batches produced using method A.

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