hw07 ChE 132C due Mar. 2, 2011
1)
The myosin catalyzed hydrolysis of ATP depends on the concentration of ATP. At 25oC
and pH 7.0, the rates are
[ATP]
7.5
12.5
20
32.5
62.5
155
320
rate
0.067
0.097
0.119
0.149
0.185
0.191
0.195
Where [ATP] is given in M and rate is given in M/s. Suppose the rate data fits a
Michaelis-Menten rate law
rate 
vmax [ ATP]
K  [ ATP]
Devise a linear regression strategy to find vmax and K and create an Excel spreadsheet for
the linear regression.
2)
The tensile strengths of 30 randomly selected graphite epoxy composite products are
tested. The sample mean and sample standard deviation are
x  38.518 and
s  2.299
Compute the p-value to test the (null) hypothesis that =40.0.
3)
Suppose you roll a six sided die n times and only once roll a six. Test the hypothesis that
this die is weighted to avoid six with the hypotheses H0: p ≥ 1/6 and HA: p < 1/6.
Compute the p-value for H0 if you find one six in n=10, 20, 30, and 40 rolls.
hw08 ChE 132C due Mar. 11, 2011
1)
Think critically about the meaning of your model, even if the p-value is tiny!
Pacansky et al. Appl. Spectr. 40, 9 (1986). Polyperflouropropyleneoxide (PPFPO) is a viscous
liquid used in electronics as a lubricant. The optical density (y) of PPFPO was measured at
different absorption band frequencies (x1) of PPFPO with different film thicknesses (x2). The
data are
‐1
x 1/(cm )
740
740
740
805
805
805
980
980
980
1235
1235
1235
x 2/m
1.1
0.62
0.31
1.1
0.62
0.31
1.1
0.62
0.31
1.1
0.62
0.31
y/arb.
0.231
0.107
0.053
0.129
0.069
0.03
1.005
0.559
0.321
2.948
1.633
0.934
a) Is this experiment designed such that nonlinear effects between thickness and frequency
would be detected (if they did exist)?
b) Create a two variable linear regression model of the type y = 0 + 1 x1 + 2 x2. The variable
y is a degree of absorbance relative to some standard surface film, i.e. a non-negative number.
Do the values predicted by your regression model make sense at each of the 12 data points?
Circle those rows of the table for which the regression model predicts y-values that are
impossible. Why is the regression model doing this, even when the F-test (computed by excel)
gives a very small p-value?
c) The model in part (b) contains three parameters. Instead, construct four fits of the type
y = k x2
where k is a coefficient determined from linear regression using only data at the kth frequency.
(1st frequency is 740cm-1, 2nd frequency is 805cm-1, etc.) Make a chart (y vs. x2) showing the
four separate models with the regression trendline for each. Edit the legend to show the
frequency, the fit equation, and the R2 statistic for each data series.