EMCH 361Lab 1Dr. Victor Giurgiutiu

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Statistics/Probability Take-Home

SUMMARY

This is a paper clip bending experiment (sample size 20). You will start the experiment in class and will continue it after class. The data to be recorded is the number of bends necessary to break the clip. This will constitute the statistical data. Based on the statistical data, you will calculate some statistical/probability results.

OBJECTIVES:

This homework explores statistics/probability principles using as an example the paper clip bending test.

TEXTBOOK REFERENCE:

Chapter 3, sections 1-5, 10-11, 14

EQUIPMENT:

Paper clips

Lock Pliers.

1.Theoretical Background:

Please see the Statistics/Probability handout.

2.Experimental Procedure:

2.1Practice Tests

Take a paper clip and bend it backwards and forward until it breaks. During the bending, count the number of bend reversals. Write down your result. Try another one. Write down your result. If you feel confident that you got it under control, proceed to the next step.

2.2Actual Tests

Select 20 paper clips that will constitute your sample. The paper clips are your test specimens. Bend them until they break. After each specimen breaks, record in Table 1 the number of bends taken to break and any comments you may have. Then proceed with the next specimen.

Note: Do your entries in pencil. Use an eraser for corrections. Preserve a neat appearance.

Table 1Experimental data

Sample # / Statistical data
(number of bends) / Comments

2.3Procedure Details

Give here details of your experimental procedure. Give sufficient information for other people to be able to reproduce your results independently by just reading this section.

3.Data Reduction

Use the data recorded in Table 1 to create a table of ranked data (Table 2). Count and enter the cumulative number of occurrences at each repeated level. (For example, if 4 samples broke after the same number of bends, say, 14 bends, count them in increasing sample order as 1, 2, 3, 4.)

Table 2Ranked data

Statistical data (number of bends) / Sample # / Cumulative number
of occurrences / Comments

4.Data Interpretation

Use the results from Table 2 to enter data in Table 3 and calculate the statistical frequency and the cumulative frequency. Because you have integer values, the statistical classes have integer labels. For example, the class containing all the samples that broke after, say, 12 bends, will be labeled ‘12’. (If you were using non-integer values, you would have to label the bin 11.5<i<=12.5)

4.1Statistical Frequency

Table 3Statistical frequency

Statistical class
(Number of bends) / Statistical frequency
(number of occurrences) / Cumulative frequency / Relative frequency / Cumulative relative frequency / Comments

4.2Statistical Characteristics of your Sample

Calculate the mean, median, max, min, and standard deviation for your data set.

Mean
median
Min
Max
Standard Deviation

4.3Histogram Chart

Draw a histogram of statistical frequency vs. number of bends to break.

Figure 1Statistical frequency (number of occurrences) vs. statistical class (number of bends to break)

4.4Relative Frequency and Normal Distribution Charts

Draw a histogram of relative statistical frequency vs. number of bends to break Superpose the curve representing the normal distribution with same mean and standard deviation.

Figure 2Sample relative frequency and normal distribution with same mean and standard deviation.

4.5Confidence Intervals

Calculate the confidence interval of using the mean and the standard deviation values found in your experiment as representative of population mean and standard deviation. Assume (though not entirely correct…) that your sample can be considered a large sample.

4.5.1Confidence interval for the mean

Assume that the sample mean, , determined in your experiment, is going to be used to represent the population mean, . Give the 95% confidence interval.

4.5.2Confidence interval for the standard deviation

Assume that the sample standard deviation, Sx, determined in your experiment, is going to be used to represent the population mean, . Give the 95% confidence interval.

5.Tips and Suggestions

5.1Calculation of Statistical Quantities

You can perform the calculation of statistical quantities in many way:

  1. Using directly the formulas
  2. Using the tabulated values given in the textbook
  3. Using statistical functions on your pocket calculators
  4. Using the built in statistical functions available in most mathematical software packages. For example, MS Excel has most of what you need for the analysis required in this homework. Explore and enjoy the MS Excel Help !!! You will find this much more fun and easier to use.

5.2Importing charts into MS Word

In performing the calculations and drawing the charts, you are encouraged to use MS Excel software or equivalent. However, your report should be in MS Word, or equivalent. When cutting and pasting from MS Excel into Word, use Edit\Paste Special\Picture. Do not use direct cut and paste, since this will import the Excel application file, increase the size of your Word file, and may produce problems. After pasting your picture, right-select the ‘Format Object’ dialog box and position the picture ‘In line with the text’. (This can be found under ‘Layout’ in Word 2000; for Word 97, uncheck the float over text check box in the ‘Position’ tab).

6.Discussion

Discuss the main findings from your experiment.

6.1Convergence of Theory and Experiments

Comment on how well does the experimental data fit the theoretical model, i.e., the normal distribution. Highlight the salient feature of your results (good features and bad features).

6.2Sources of Errors

List the probable sources of uncertainty in this lab. Explain how each factor may affect the results and list them in terms of significance.

7.Conclusions

7.1Conclusions about the Experiment

Tell if the experiment was or was not conducted with professionalism and if the data collected during the experiment should or should not be credible.

7.2Conclusions about the Sampled Specimens

Conclude if the sampled specimens behave or do not behave in accordance with expectations.

7.3Suggestions for Improvement

All these suggestions listed below are highly valuable to the future experimentalists. Be generous in your suggestions.

7.3.1Suggestions for improvement of the experiment

Give suggestions about how to improve the experimental procedure and the collection of samples. Explain how would the experiment be conducted better, given a second chance.

7.3.2Suggestions for improvement in the data reduction

Give suggestions for improvement of the data reduction process. Suggest software or algorithms that might be useful to future researchers, if you know of can think of any.

7.3.3Suggestions for improvement in data interpretation

Suggest better and more effective ways of data interpretation, if you know, or can think of any.

Lab 1 handout.doc11/25/2019