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Transcript
```AP Statistics
12.2A Assignment
1. Mrs. Hanrahan’s Pre-Calculus class collected data on the length (in centimeters) of a pendulum and the time (in
seconds) the pendulum took to complete one back-and-forth swing (called its period). Here are their data:
Length (cm)
16.5
17.5
19.5
22.5
28.5
31.5
34.5
37.5
43.5
46.5
106.5
Period (s)
0.777 0.839 0.912 0.878 1.004 1.087 1.129 1.111 1.290 1.371 2.115
A. Make a reasonably accurate scatterplot of the data, using length as the explanatory variable. Describe what you
see.
There is a strong positive slightly curved relationship between
length and period with one very unusual point in the top-right
corner.
B. The theoretical relationship between a pendulum’s length and its period is period 
2
g
length where g is a
constant representing the acceleration due to gravity (in this case, g = 980 cm/s2). Use a transformation to
linearize the curved pattern in the graph.
The scatterplot shows
length vs period.
C. Give the equation of the least-squares regression line. Define any variables you use.
yˆ  0.086  0.210 x
ŷ is the predicted period and x is the length of the pendulum
D. Use the model from part C to predict the period of a pendulum with length 80 centimeters. Show your work.
yˆ  0.086  0.210 80  1.8 seconds
2. If you have taken a chemistry class, then you are probably familiar with Boyle’s law: for gas in a confined space kept
at a constant temperature, pressure times volume is a constant  in symbols, PV  k  . Students collected the
following data on pressure and volume using a syringe and a pressure probe.
Volume (cubic centimeters)
6
8
10
12
14
16
18
20
Pressure (atmospheres)
2.9589 2.4073 1.9905 1.7249 1.5288 1.3490
1.223
1.1201
A. Make a reasonably accurate scatterplot of the data, using length as the explanatory variable. Describe what you
see.
There is a strong negative curved relationship between volume
and pressure.
B. The theoretical relationship between the pressure and volume of the gas is PV  k , we can divide both sides of
this equation by V to obtain the theoretical model P 
k
1
, or P  k   . Use a transformation to linearize the
V
V 
curved pattern in the graph.
The scatterplot shows
1
vs pressure
volume
C. Give the equation of the least-squares regression line. Define any variables you use.
15.897
x
ŷ is the predicted pressure and x is the volume
yˆ  0.368 
D. Use the model from part C to predict the pressure in the syringe when the volume is 17 cubic centimeters.