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course PHY 201
10/05/2011 5:28 PMQuestion at end of document.
testing hypothesis time intervals
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PHY 201
Your 'testing hypothesis time intervals' report has been
received. Scroll down through the document to see any comments I
might have inserted, and my final comment at the end.
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10/04/2011 2:46 PM
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45 minutes
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Hypothesis Testing
Suppose we have observed the following time intervals:
.925, .887, .938, .911, .925, .879, .941
where the time intervals are in seconds.
• The mean of these numbers is .915.
• The (mean) average deviation of the numbers from this
mean is .020.
• The standard deviation of this distribution is .024.
If these time intervals were recorded by an accurate instrument,
an instrument that is accurately calibrated and without any
distortion in its scale of measurement, set up and utilized in
such a way that there is no systematic bias in the readings, then
we expect that the time interval between the events we are
measuring lies within one standard deviation of the mean.
That is, we expect that the actual time interval `dt lies between
(.915 sec - .024 sec) and (.915 sec + .024 sec).
We could write this as an inequality
.915 sec - .024 sec < `dt < .915 sec + .024 sec,
meaning the same thing as
.891 sec < `dt < .939 sec.
We would then be able to report our result as .915 seconds +-.024
seconds.
Your hypothesis:
In this experiment, which uses the TIMER program, you are going
to click the mouse as quickly as possible with the index finger
of your dominant hand, then you are going to click it as quickly
as possible with the fist of your non-dominant hand.
• Do you think the index finger is be 'quicker' than the
fist?
• Do you think the fist is be 'quicker' than the index
finger?
• Do you think the index finger and the first are equally
quick?
State which you think is the case:
Your answer (start in the next line):
I think the index finger of my dominant hand will be faster than
the fist of my non-dominant hand.
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• The statement you just made is your hypothesis for this
experiment.
It should take you only a few minutes to get your data for this
experiment:
• Open the TIMER program and do 10 clicks, as fast as
possible, using the index finger of your dominant hand (i.e.,
your right hand if you are right-handed, your left hand if you
are left-handed).
• Do this until you have managed 10 good, quick clicks,
with no 'misfires'.
• Copy the relevant portion of the TIMER output into the
data analysis program and eliminate everything but the 10 time
intervals, one to each line.
• Find their mean and standard deviation, and note these
results.
• Copy your 10 time intervals into the space below:
Your answer (start in the next line):
.1835938, .1875, .1875, .171875, .171875, .203125, .171875,
.21875, .1875, .203125
#$&*
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Now repeat, but instead of the index finger of your dominant hand
use the fist of your non-dominant hand. Use your fist gently.
Don't hit the mouse hard enough to damage it or cause it to start
moving around.
Put this information into the data analysis program at
•
http://www.vhcc.edu/dsmith/genInfo/labrynth_created_fall_05/levl1
_15\levl2_51/dataProgram.
exe
and use the program to find the mean and standard deviation and
note these results.
Copy your 10 time intervals into the space below:
Your answer (start in the next line):
.171875, .15625, .1875, .1679688, .171875, .171875, .171875,
.15625, .171875, .15625
#$&*
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Report the mean and standard deviation of your index-finger data
in the first line below, in comma delimited format. Report your
fist data in the second line, in the same format.
Your answer (start in the next line):
0.1887, 0.01563
0.1684, 0.009822
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Using the form mean +- standard deviation, report in the first
line below the result of your index-finger observations.
For example, if the mean was .27 seconds and the standard
deviation was .05 seconds, then you would report
.27 +- .05
in your first line.
In the second line report, using the same format, the result of
your 'fist' observations.
Your answer (start in the next line):
0.1887 +- 0.01563
0.1684 +- 0.009822
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You will now report the same information by reporting upper and
lower bounds.
If for example the result of an observation of a time interval
was (.27 +- .05) sec, the lower and upper bounds on the time
interval would be
• lower bound - (.27 - .05) sec = .22 sec and
• upper bound (.27 + .05) sec = .32 sec.
In the first line below report the lower and upper bounds of the
'index finger' results. For example if your results were as in
the example given here, you would report
.22, .32.
In the second line do the same for your 'fist' results.
Your answer (start in the next line):
0.20433, 0.17307
0.178222, 0.158578
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Sketch in your lab notebook a number line representing time
intervals. Your sketch might look something like the figure
below.
Sketch on your number line the interval between mean - standard
deviation and mean + standard deviation from your 'index finger'
results. For example the number-line representation of the result
.27 +- .05 would be as indicated below. The interval is shaded
(here it is shaded in blue) and set off with parentheses.
Sketch also, on the same number line, the interval corresponding
to your 'fist' results.
Possible examples of the way a sketch might come out are depicted
below:
The two intervals might be completely separate:
The two intervals might overlap:
One interval might even contain the other:
So, your two number-line intervals might overlap, or they might
be completely separate.
For example, if your two results were .27 +- .05 and .37 +- .03,
then one of your number-line intervals would run from .22 to .32
and the other would run from .34 to .41.
• In this case we would say that the two number-line
intervals are separated by the number-line interval from .32 to
.34. We will call this the interval of separation, and the bounds
on this interval of separation are .32 and .34.
On the other hand if your two results were .27 +- .06 and .37 +-
.06, then one of your number-line intervals would run from .21 to
.33 and the other would run from .31 to .43.
• In this case we would say that the two number-line
intervals overlap on the number-line interval from .31 to .33. We
will call this the interval of overlap, and the bounds on this
interval of overlap are .31 and .33.
Report the nature of your intervals below:
• If your number line intervals are completely separate,
enter in the first line of the space below the bounds on the
interval of separation.
• If your number line intervals overlap, enter in the first
line of the space below the bounds on the interval of overlap.
• In the second line specify by the word 'separation' or
'overlap' whether the intervals are separate or overlapping.
Your answer (start in the next line):
0.173, 0.178
overlap
#$&*
#$*&
The results you obtained in this experiment are indications of
what we will call 'finger repeat time' and 'fist repeat time'.
Let's assume that you have an actual neurologically controlled
repeat time for your index finger, and one for your fist. This is
a very questionable assumption, but for the purposes of our
analysis here let's make it.
The 10 results from each trial, on which you based your analysis
here, comprise a limited sample of your actual repeat times.
Assume that you have a specific 'actual' index finger repeat time
(another questionable assumption).
• Assume furthermore that it is represented somewhere in
the number-line interval you obtained for your index-finger
results, and
• Similarly assume that your 'actual' fist repeat time is
represented somewhere in its number-line interval:
Based on these assumptions:
• Is it possible for your finger time to be less than you
fist time?
• Is it possible for your fist time to be less than you
finger time?
• Is it possible for both times to be identical, within the
limits of accuracy of the TIMER?
• Can you or can you not conclude that your index-finger
response time is different from your fist response time?
Your answer (start in the next line):
It is slightly possible for the finger time to be less than the
fist time.
It is highly possible for the fist time to be less than the
finger time.
It is slightly possible for the times to be identical.
I can conclude that my finger time was slower than my fist time.
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Based on the preceding set of questions, do your results support
or fail to support your original hypothesis? Explain thoroughly
how your results lead you to accept or reject your hypothesis.
Your answer (start in the next line):
My results fail to support my original hypothesis. Based upon
the recorded times, means, deviations, and the number line I have
to conclude my finger click time is slower than my fist click
time.
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*#&!
@& Your calculations appear to be correct, and everything is well
done.
However you cannot draw the conclusion you state.*@
@& According to the test used it is possible that the two are the
same, and you cannot conclude, with the very high level of
certainty implied by this test, that they are different.
With a difference test, at a lower level of certainty, you could
draw the conclusion that the two times are different.*@
*#&!
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Based on the preceding set of questions, do your results support
or fail to support your original hypothesis? Explain thoroughly
how your results lead you to accept or reject your hypothesis.
Your answer (start in the next line):
It does in fact conclude my hypothesis in stating that the finger
would be quicker. When I used the TIMER program to time the
clicks between my finger and fist it was evident that my finger
was quicker. I however believe this only to be true under the
circumstances that using my fist seemed awkward.
#$&*
*#&!*#&!*#&!
@& At least one other lab has been submitted by a different
individual with exactly the same data.
It's OK to work on labs with other people, but there is no reason
on this lab, where it takes less than a minute to get the data,
that different people would use the same data.
Please take another set of data, independent of the data
collected by others, and submit this lab once more.*@
&&&&
What is this note about resubmitting a new lab???
I can assure you that I have worked with no one else on any of my
assignments.
&&&&"
@& This note was apparently misplaced. Your data and your work have not been duplicated by anyone else, and everything looks good.
However note that the intervals overlap, so you cannot draw your stated conclusion with the (very high) level of certainty provided by this test.
Your lab should have been posted with a similar note.*@