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levels of the Tower of Pisa (which was leaning even then) and timed its
descent by counting his pulse. The following data are measurements
Galileo might have made.
Find the power curve formulas that best expresses h as a function of t (h =
At
B
).
The formula that best expresses h as a function of t is
We know, as Galileo did not, that in fact h is proportional to t
2
.
Standard Error of the Mean
The standard error of the mean is a measure of how reliable the mean of a
sample (
X
) is as an estimator of the mean of the population from which the
sample was drawn.
To calculate the standard error of the mean:
t
(pulses)
2 2.5 3.5 4 4.5
h (feet) 30 50 90 130 150
Keystrokes Display
CLEAR
30
2
1.00 First pair data input.
50
2.5
2.00 Second pair data input.
90
3.5
3.00 Third pair data input.
130
4
4.00 Fourth pair data input.
150
4.5
5.00 Fifth pair data input.
1.00
Correlation coefficient (between In
y and ln x).
0
7.72 Value of A.
1 0
1.99 Value of B.
h 7.72t
1.99
=