The article “Optimization of Medium Composition for Lipase

Chapter 7, Problem 8SE

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The article “Optimization of Medium Composition for Lipase Production by Candida rugosa NCIM 3462 Using Response Surface Methodology” (A. Ragendran and V. Thangavelu, Can J. Microbiol, 2007:643–655) describes a series of experiments in which lipase was produced from a bacterial culture. In each experiment, the rate of lipase production (in \(\mu\mathrm {mol}\) per ml enzyme per minute) and the cell mass (in g/L) were measured. The results are presented in the following table.

\(\begin{array}{cc||cc||cc||cc}
\hline \begin{array}{c}
\text { Cell mass } \\
(\boldsymbol{x})
\end{array} & \begin{array}{c}
\text { Lipase } \\
(\boldsymbol{y})
\end{array} & \begin{array}{c}
\text { Cell mass } \\
(\boldsymbol{x})
\end{array} & \begin{array}{c}
\text { Lipase } \\
(\boldsymbol{y})
\end{array} & \begin{array}{c}
\text { Cell mass } \\
(\boldsymbol{x})
\end{array} & \begin{array}{c}
\text { Lipase } \\
(\boldsymbol{y})
\end{array} & \begin{array}{c}
\text { Cell mass } \\
(\boldsymbol{x})
\end{array} & \begin{array}{c}
\text { Lipase } \\
(\boldsymbol{y})
\end{array} \\
\hline 4.50 & 2.06 & 3.98 & 2.10 & 3.65 & 2.20 & 4.15 & 3.75 \\
4.68 & 2.10 & 4.72 & 2.75 & 4.23 & 2.30 & 4.30 & 3.15 \\
5.40 & 3.15 & 3.41 & 2.80 & 4.10 & 2.40 & 4.90 & 5.10 \\
5.45 & 4.10 & 4.80 & 4.60 & 5.03 & 4.75 & 5.23 & 5.04 \\
4.20 & 2.20 & 3.60 & 2.50 & 4.19 & 3.15 & 5.40 & 4.96 \\
4.12 & 3.20 & 4.95 & 4.10 & 4.40 & 3.90 & 4.85 & 5.00 \\
4.00 & 2.85 & 3.25 & 2.15 & 3.92 & 3.20 & 5.10 & 4.92 \\
4.41 & 4.50 & 4.40 & 4.40 & 3.50 & 2.10 & 4.94 & 4.98 \\
\hline
\end{array}\)

a. Compute the least-squares line for predicting lipase production from cell mass.

b. Compute 95% confidence intervals for \(\beta_0\) and \(\beta_1\).

c. In two experiments, the cell masses differed by 1.5 g/L. By how much do you estimate that their lipase productions will differ?

d. Find a 95% confidence interval for the mean lipase production when the cell mass is 5.0 g/L.

e. Can you conclude that the mean lipase production when the cell mass is 5.0 g/L is less than 4.4? Explain.

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