1. Retrieve the data file EXCHNGRT.XLS
from the class folder. This is a population
of the
daily exchange rates between the French franc and the U.S. dollar,
specifically,
each value specifies the number of francs required to purchase one
dollar.
2. Use AVERAGE and STDEVP
to find the mean and standard deviation of this
population.
Then use HISTOGRAMS in the ToolPak to construct a histogram
of the
population. Recall that the bins are the upper limits of each class--any
values
larger than the upper limit will appear in a class of larger values. Record
the mean,
standard deviation, and pattern of the population. You will make
comparisons
with these three pieces of information as you proceed. (Construct
another
histogram with different class sizes to be sure that the choice of classes
does
not distort the pattern of the data.)
3. Use the SAMPLING function
in the ToolPak to select a random sample of 36
exchange
rates (we allow values to repeat in the sample). What is?
Is it
the same
as m? Should
we expect = m?
Should we expect
to be
close
to m
? Explain.
4. What is S (STDEV) for the sample
from Question 3? Is it the same as s
?
Is it
close?
What should we expect here? Explain.
5. Use the bins from Question 1
to construct a histogram and determine the pattern
of the
36 sample values. Compare the results to the population. Are they similar
or dissimilar?
Do you think your sample is representative of the population?
6. What is the standard error of
the mean for samples of 36 observations from this exchange rate
population?
A standard deviation measures the dispersion of values in a data
set.
Describe the different data sets when we compute s,
S, and the standard error. What is the
symbol
for the standard error of the mean?
7. If we use S to estimate s,
what does estimate? Compute
from your
sample
and compare it with the actual population parameter that we estimate
with
it. Are the two close?
8. Assume you know the population
mean and standard deviation. Suppose you
need
to select a random sample of 36 exchange rates (with replacement) from
the population.
What is the approximate probability the mean of your sample will
be greater
than 5? Draw a diagram, then use EXCEL to obtain an answer.
9. Print your sample values along
with their histograms and statistics. Bring these to
the next
class so that you can complete the next worksheet.
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