Sampling Distribution of  Central Limit Theorem,
and Standard Error of the Mean
Worksheet 17

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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