PURPOSE:
Estimate the statistical properties of a population and a sample to evaluate the dimensional characteristics of the nuts.
OBJECTIVES:
1. Review the use of micrometers to measure the characteristic dimensions of the given nuts.
2. Evaluate the statistical properties of a population of the nuts.
3. Evaluate the statistical properties of a sample of nuts to infer data about the entire population. Did the factory create all the nuts equally?
PROCEDURES:
I. Collect the data
1. Each team will be provided with a group of nuts.
2. Measure the width of each nut using the micrometer. Record this data in an Excel spreadsheet. (NOTE: Begin recording information about your experiment in your Lab Notebook. Although this data can be directly entered into Excel, you should record notes about your experiment in your lab notebook, including procedures you have completed or steps you could forget later.)
3. Collect the data from the other teams in your lab section so that you have a table with measurements for all of the nuts. This will be your data population.
4. Sort the complied data of the measured values in ascending order.
What would be the best estimate of the thickness of the population? Why? To answer these questions, we need to statistically analyze the data.
II. Reduce the data as follows:
A. Calculate the mean, median, mode and standard deviation of the population, assuming that the population is the total number of nuts measured by the entire class.
B. Record the sources of error for your measurements and the uncertainty that comes from reading the instrument.
C. Use Chauvenet's criterion to test the data points for possible inconsistencies.
D. After testing the data, calculate the new mean and standard deviation for the adjusted nut population.
E. Construct a histogram for the data range of the nut measurements, divided into K segments (bins). Explain how you determined K and the intervals on your histogram.
F. Overlay the theoretical Gaussian distribution curve with the histogram for the nut measurements.
G. Draw the cumulative frequency diagram for the measured data.
H. Using the random number generator, compile random numbers to pair against the thickness measurements. Sort the random numbers in ascending order. Plot the nut measurements on the abscissa and the random numbers on the ordinate.
I. Fit a linear least squares regression equation to the data plotted in the above step using the functions in Excel and the trend line in Excel's graphing function.
J. Compute the correlation coefficient for each regression using the function in EXCEL. Is the line a "good" fit?
K. Randomly select two groups of 10 measurements from the population using the Sampling tool in the Data Analysis Toolpak in Excel.
L. Compute the mean and standard deviation of each sample.
M. Find the standard deviation of the mean for the samples. What do the values indicate? How do they compare?
What do the results tell you about the samples in relation to the population they were drawn from?
N. Use the t-test in Excel to examine the differences between the sample means. Based on the results, what can you predict about a third sample drawn from the population? Can you infer anything about the population based on these results?
O. Take 3 random samples of 10 from the entire population. Perform a one way ANOVA test on the samples and determine if the results are significant. Are they statistically equivalent?
P. Compare the uncertainty determined through experimental methods (e.g. from device) and the uncertainty determined from the statistical analysis performed.