# Tutor profile: Stephen C.

## Questions

### Subject: Microsoft Excel

Describe how to manually calculate a 95% confidence interval around a known mean in Excel, and how to confirm that this calculation is correct using native Excel functions.

Begin by calculating the variance: take the difference between each data point in your data set and the mean of the data. Square each difference, and then sum the differences. Your variance will be this sum divided by N-1, where N is the number of observations in your data set. To calculate the standard error, take the square root of the variance and divide by the square root of N. Then, refer to a t-table for the appropriate t value for the desired confidence interval. In our case, consider a data set with 50 data points, giving 49 degrees of freedom. t is then 2.01 for a confidence interval of 95%, and the limits of our confidence interval will be given by: Lower limit: Mean - (2.01 * standard error) Upper limit: Mean + (2.01 * standard error) To verify this calculation is correct, we use Excel's native CONFIDENCE.T() function. It takes three arguments: alpha, which is .05 for a 95% CI, the standard deviation of our data set, which can be calculated by hand or using the native STDEV() function, and the number of observations in our data set.

### Subject: Medicine

Explain the concept of preload dependence in heart failure, and describe why it has clinical importance.

The Frank-Starling relationship describes how the filling of the heart's ventricles with blood affects the ability of the cardiac muscle to contract--in other words, how changes in preload lead to changes in stroke volume. At healthy, physiologic levels of filling, increases in preload tend to lead to increases in stroke volume. As the heart fails, a paradox may begin to develop: even as extra-cardiac symptoms of congestive heart failure may manifest clinically, such as peripheral edema and pulmonary congestion, the heart's decreased ability to generate adequate forces of contraction may mean that the heart is more dependent than ever on its preload. Thus, the desire to diurese a patient with significant edema must be balanced against concern that depleting the patient's volume could cause decompensation of their failing heart.

### Subject: Biochemistry

Explain in words the significance of the Michaelis constant, Km, in Michaelis-Menten enzyme kinetics.

The Michaelis constant Km is the concentration of substrate required for a reaction described by Michaelis-Menten kinetics to reach one half of its maximum reaction velocity, Vmax. Briggs and Haldane offered a derivation of the relationship between Km and Vmax. Critically, they make a steady-state assumption for the reaction--that is, product formation must be linear over time in order for Michaelis-Mentin kinetics to approximate the actual reaction. Km can also be thought of as a binding affinity that the enzyme has for a substrate. In other words, a lower Km implies a lower concentration of substrate required for a reaction to reach one half its maximum velocity, which implies a higher binding affinity between the enzyme and the substrate. Similarly, a greater Km implies a higher concentration of substrate required for a reaction to reach one half its maximum velocity, and a relatively lower binding affinity between the enzyme and substrate.

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