The article “Reaction Modeling and Optimization Using Neural Networks and Geneti

Question

The article “Reaction Modeling and Optimization Using Neural Networks and Genetic Algo- rithms: Case Study Involving TS-1-Catalyzed Hydroxylation of Benzene” (S. Nandi, P. Mukherjee, et al., Industrial and Engineering Chemistry Research, 2002:2159-2169) presents benzene conversions (in mole percent) for 42 different benzenehydroxylation reactions. Ideally, in order to be used in many industrial applications the mean conversion needs to be greater than 30. Do we have data that supports this? 42 different benzenehydroxylation reaction conversions are listed below.

85, 30, 28, 12, 74, 16, 81, 73, 27, 56, 85, 50, 20, 55, 78, 13, 42, 39, 16, 37, 73, 47, 73, 50, 46, 20, 76, 58, 22, 19, 55, 35, 42, 57, 23, 35, 83, 19, 17, 42, 18, 18

(a) Based upon the data, which method should you use to analyze the data? Use R to generate appropriate plots, and conduct statistical tests and provide answers for other appropriate computational methods to justify your answer.

The rest of this problem should be done by hand along with the t-table only. Do not use R to get the final answer for the P-value

(b) State the null and alternative hypothesis in words and symbols.

(c) Using the method that you selected and justified, carry out that method, assuming = 0.05. However, do not compute the exact P-value, instead use the rejection region approach to conduct the test. Provide a plot of the t-distribution with the critical value(s) (found using the t-table) that define the rejection region(s) and indicate where the test statistic is located.

(d) State the conclusion of the test and provide an interpretation of the conclusion in the context of this particular problem. Specifically, do we have statistical evidence that these benzenehydroxylation reactions meet industrial specifications?

Explanation / Answer

Below are the null and alternate hypothesis
H0: mu = 30
H1: mu > 30

sample mean = 42.52380952
sample std. dev. = 22.96653881
n = 42

Test statistics, t = (42.5238 - 30)/(22.9665/sqrt(42)) = 3.534

p-value = 0.0005

As p-value is less than the significance level of 0.05, we reject the null hypothesis.
This means from the given sample there is significant evidence to conclude that benzenehydroxylation reactions meet industrical specifications.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.