LAB 7 FOR EXCEL 2007
SAMPLING DISTRIBUTIONS OF STATISTICS
NAME__________________________LAB TIME_________PHYS ROOM NO____________
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Every statistic (such as the Sample Mean, the Sample Standard Deviation, the Sample
Variance ) has a SAMPLING DISTRIBUTION which shows the pattern of variation of
the statistic when the same population is sampled over and over and over.
In this lab we will use Excel’s random number generator to draw 2500 observations from
a population which has a Normal Distribution with a mean = 100 and a standard
deviation = 5.
What should be the approximate values of the smallest and largest of these 2500? Use +
and – 3 sigma as the approximate “edge” of the normal distribution.
Minimum should be approximately ( mean – 3 std dev) = ____________
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Maximum should be approximately ( mean + 3 std dev)= ____________
In Excel, do Data>Data Analysis>Random Number Generator.
In the window which appears, set Variables = 5, Number of Random Numbers = 500,
Distribution = Normal, Mean = 100, Standard Deviation = 5, Random Seed = 25674,
click on Output Range, and enter A2 in the box beside the output range. Check that the
random seed has not changed and then click OK.
On line 1 of Excel, number the columns A through E as 1,2,3,4,5
We now have 500 lines of 5 observations each in Columns A through E.
We will treat each line as a random sample of size = 5. So we have 500 random samples
of size =5 in rows 2 through 501.
CALCULATION OF MEAN, STANDARD DEVIATION AND RANGE FOR EACH
SAMPLE:
In G1 enter sample mean; in H1 enter sample std dev; in I1 enter sample max, in J1
enter sample min; in K1 enter sample range.
In G2 calculate the mean for a2:e2. (Use the excel AVERAGE (a2:e2)
In H2 calculate the standard deviation of a2:e2. Use excel STDEV (a2:e2)
In I2 calculate the maximum for a2:e2. Use excel MAX (a2:e2)
In J2 calculate the minimum for a2:e2. Use excel MIN (a2:e2)
In K2 calculate the sample range, I2-J2.
Copy G2:K2 down through line 501.
In G503 calculate the overall mean of the 500 sample means. (Use excel AVERGE
(g2:g501)
Enter the overall mean of the 500 sample means _________________
Assuming that the POPULATION MEAN = 100, calculate the percent error for the mean
of the 500 sample means using (G503-100)/100*100% :_________________
Does the sample mean appear to be an unbiased statistic?__________________
In G504 calculate the standard deviation of the 500 sample means. Use excel STDEV
(g2:g501)
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Enter the standard deviation of the 500 sample means:___________________
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Theory says the standard deviation of the sample means = Population std dev / sqrt (n). or
5 / sqrt(5) = 2.236.
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Calculate the percent error for the value in step 22 vs the theoretical value in step 23
using (G504-2.236)/2.236*100% : ________________
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In H 503 calculate the mean of the 500 sample standard deviations: _________________
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Assuming that the POPULATION STANDARD DEVIATION = 5, calculate the percent
error in the mean of the 500 sample standard deviations: ________________________
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Does the sample standard deviation appear to be an unbiased statistic? ______________
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Theory says that the sample standard deviation will average 6% lower than the
population standard deviation when the sample size = 5. If this is true, the mean of the
500 sample standard deviations should have been 4.7000.
Calculate the percent error between the actual mean of the 500 sample standard
deviations (step 25) and the predicted value given in step 28:
____________________________
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In K503 calculate the mean of the 500 sample ranges:__________________________
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Theory says that the sample range for a sample size = 5 will average 2.326 times the
population standard deviation, or 5 (2.326) = 11.63.
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Calculate the percent error for the actual mean of 500 sample ranges (step 30 ) vs the
theoretical value (step 31): ____________________
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DRAWING A HISTOGRAM OF THE SAMPLE MEANS
Do Tools>Data Analysis>Histogram and click OK.
Input range: G2:G501.
Click on Output Range, and in the box enter M1.
Click on Chart Output, and click OK.
Close up the spaces between the histogram bars. (right click on any bar, click on Format
Data Series, click on Options and bring Gap down to 0.
Size the histogram. Correct the title to read Histogram Of Sample Means.
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Comment on the shape of the histogram: _____________________________________
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Print the histogram to turn in with these answers.