Knoop Microhardness Experiment



Lab 1 -- 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

Theoretical Background:

Please see the Statistics/Probability handout.

Table of Contents

1. Theoretical Background: 2

2. Experimental Procedure: 3

2.1 Practice Tests 3

2.2 Actual Tests 3

2.3 Procedure Details 4

3. Data Reduction 5

4. Data Interpretation 6

4.1 Statistical Frequency 6

4.2 Statistical Characteristics of your Sample 6

4.3 Histogram Chart 7

4.4 Relative Frequency and Normal Distribution Charts 7

4.5 Confidence Intervals 8

4.5.1 Confidence interval for the mean 8

4.5.2 Confidence interval for the standard deviation 8

5. Tips and Suggestions 9

5.1 Calculation of Statistical Quantities 9

5.2 Importing charts into MS Word 9

6. Discussion 10

6.1 Convergence of Theory and Experiments 10

6.2 Sources of Errors 10

7. Conclusions 10

7.1 Conclusions about the Experiment 10

7.2 Conclusions about the Sampled Specimens 10

7.3 Suggestions for Improvement 10

7.3.1 Suggestions for improvement of the experiment 10

7.3.2 Suggestions for improvement in the data reduction 10

7.3.3 Suggestions for improvement in data interpretation 10

Experimental Procedure:

1 Practice 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 Actual 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 1 Experimental data

|Sample|Statistica|Comments |

|# |l data | |

| |(number of| |

| |bends) | |

|1 |8 | |

|2 |9 | |

|3 |9 | |

|4 |9 | |

|5 |10 |I think it slipped from my hands |

|6 |9 | |

|7 |7 | |

|8 |9 | |

|9 |10 |I think it slipped from my hands |

|10 |8 | |

|11 |8 | |

|12 |7 | |

|13 |8 | |

|14 |8 | |

|15 |9 | |

|16 |9 | |

|17 |6 |I must have put my nail into it |

|18 |7 | |

|19 |10 |I think it slipped from my hands |

|20 |9 | |

3 Procedure 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.

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 2 Ranked data

|Statistic|Sample|Cumulati|Comments |

|al data |# |ve | |

|(number | |number | |

|of bends)| |of | |

| | |occurren| |

| | |ces | |

|6 |17 |1 | |

|7 |7 |1 | |

|7 |12 |2 | |

|7 |18 |3 | |

|8 |1 |1 | |

|8 |10 |2 | |

|8 |11 |3 | |

|8 |13 |4 | |

|8 |14 |5 | |

|9 |2 |1 | |

|9 |3 |2 | |

|9 |4 |3 | |

|9 |6 |4 | |

|9 |8 |5 | |

|9 |15 |6 | |

|9 |16 |7 |This is where most of the data seems to be |

|9 |20 |8 | |

|10 |5 |1 | |

|10 |9 |2 | |

|10 |19 |3 | |

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 ................
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