The lab is designed to remind you how to work with scientific data (including dealing with uncertainty) and to review experimental design.

Transcription

1 Name: Partner(s): Lab #1 The Scientific Method Due 6/25 Objective The lab is designed to remind you how to work with scientific data (including dealing with uncertainty) and to review experimental design. Uncertainty and Error Suppose you read a study in a magazine stating that in the general population 20-30% of people have ear piercings and 1-3% of people have body piercings. Scientists would write this as 25 +/- 5% of people have ear piercings. 2 +/- 1% of people have body piercings. The first number is the result, and the second number is the random error in the result (sometimes also called the random uncertainty). Random error indicates how the results might change if you did the survey many times. Usually, if you repeat the survey, your results will agree with the number quoted within the error. Generally, errors are quoted as percentages such that: percent error = 100 x (error / total). Through most of this course we will ask you to find your uncertainty. Often this is simple enough. If you make a measurement your random uncertainty is the smallest value that you can measure. If you are using a ruler you may be only able to tell things down to the nearest mm. In that case you would record your uncertainty as: +/- 1mm. Other times, you will be recording a number of data points. In this case, your random uncertainty is the scatter of your data. For that your random uncertainty is how high above and below an average value your data falls. For example you time how many seconds it takes a rock to fall to the ground five times and measure: 5.0, 5.1, 4.9, 5.2, 4.8. You could report this as 5.0 +/- 0.2 seconds. In some cases, as in this assignment, your errors come from sampling a number of things, essentially an error in counting. The concept is that you are drawing your data points from Astronomy Introduction to Astronomy

2 a larger sample and somebody else doing the same experiment would draw a different data points and get a different answer thus leading to uncertainty between the answers. The equation for sampling error has been determined statistically to be: error = number To summarize random error: Measurement: smallest measurement one can determine Data scatter: amount off of an average Counting: square root of the number sampled There is another type of error, systematic error. This would be the case if all of your values were too big, or too small, instead of fluctuating up and down. Systematic error often comes from a bias in your methods, or equipment, say using a meter stick that isn t really a meter to measure things. In a few questions you will be asked to compare numbers. To compare two numbers scientifically, you must see if they agree within their respective uncertainties. It s not enough to say that two numbers are close together unless they are within their uncertainties of each other. So the answer to this type of question involves a little math. To compare two numbers: If A B < (uncertainty in A + uncertainty in B) then the two numbers are in agreement. Notice nowhere do the words human error show up. Please don t ever use them. Instead of listing your source of error as human, explain what specifically was the source. Astronomy Introduction to Astronomy

3 Questions The following questions are based the hypothetical magazine survey on the percent of the general population with ear and body piercings. You will be asked questions on designing an experiment to reproduce the results and interpreting the error. Use the following table to record your results. Type of Piercing % From the class survey % Error from the class survey % From the UW survey % Error from the UW survey % From Magazine Ear Piercing 25% 5% Body Piercing 2% 1% % Error From Magazine 1. (1 pt) Suppose you want to know the percentage of people in this class (teaching, auditing and enrolled) with ear/body piercings and to compare these results to the results of the survey. State a reasonable hypothesis. 2. (1 pt) How will you collect the necessary data? 3. (5 pts) Using your desired method, find out how many people in the class have ear and body piercings. Total Number of People Ear Piercing Body Piercing Number Percent Error Percent Error Transform the number of ear and body piercings into percents and fill in the appropriate results column of the table directly above and table at the top of the page. Use the correct number of significant figures! Astronomy Introduction to Astronomy

4 4. (2 pts) What sort of errors could be associated with this data? Consider such things such as whether anyone could have been lying, and whether everyone is present. Hint: This will probably not be a sampling error as you are probably not sampling a small portion of the class in order to determine the data for the whole class. Transform your errors into percent errors and fill in the appropriate error column of the two tables on page 3. Use the correct number of significant figures! 5. (1 pt) Now, suppose you were to extend your survey to find out if the numbers from the magazine survey on piercings are correct for the population of students at the UW. Write a new hypothesis that compares the the rate of piercings at the UW to that in this classroom and to that of the general population (as determined from the magazine survey). 6. (1 pt) Devise a method to collect a data set to test your hypothesis. 7. (1 pt) How would you revise your plan if you only had two hours to collect the data? 8. (1 pt) Devise an alternate plan in case the observations you want to make are impossible because you are locked in a high tower with no or cell phone, just a window to look out of. Astronomy Introduction to Astronomy

5 9. (1 pt) What is the problem with including only a small number of people in your sample? 10. (1 pt) What problems might occur if you only chose to look for subjects in a trendy cafe? 11. (2 pts) For questions 7-10 above, explicitly explain how similar types of issues could apply in astronomical research 12. (1 pt) How are the errors caused by the biases in questions 9 and 10 different? Which has a higher random error and which has a higher systematic error? Astronomy Introduction to Astronomy

6 13. (1 pt) Suppose you collect data on 523 students with the plan of extrapolating to the entire UW population. If the percentages from the magazine survey are correct (25% and 2%), what numbers of students with each type of piercing do you expect? 14. (4 pts) Here are the hypothetical results from your new survey of 523 university students: 523 Students in total 138 Students with ear piercings 34 Students with body piercings Fill in the percentages of students in your survey with ear and body piercings in the table at the top of page 3. Use the correct number of significant figures! 15. (1 pt) Your set of 534 students is a sample of the entire UW population and a different set of 534 UW students would give slightly different results. Using the formula for sampling errors given in the background, find the random error in your results. Convert your error to percentage error and fill in the appropriate column of the table. Again, use the correct number of significant digits! 16. (1 pt) Did the UW study have larger or smaller error than the ones the magazine published? 17. (1 pt) Did the magazine s survey use a larger or smaller sample than yours? (This is a quantitative question, and the answer can be derived from your solutions to questions 13 and 14.) 18. (6 pts) On a separate sheet of paper, graphically display the results for all three surveys. Bar graphs and pie charts are both good options but you are encouraged to be creative here and come up with a completely different method. Consider such things as whether you want to display all the data on one chart, two, three or even six, and how you can use color effectively. Make sure to include the error in some form and label everything clearly. You are welcome to either use a graphing program such as Excel or to draw the graph neatly by hand. If you are working in a group, you only need to turn in one graph for the entire group. Astronomy Introduction to Astronomy

7 19. (2 pts) Compare the hypothetical results of the UW survey with those from the general population that were reported in the magazine study. Use the equation for the background for comparing with uncertainties. a. Is the percentage of students with ear piercing significantly different from the variation given in the study in the magazine? b. Is the percentage of students with body piercings significantly different from the variation given in the study in the magazine? 20. (1 pt) Explain any apparent differences between the UW survey and the magazine study in terms of possible differences between students and the general population. 21. (1 pt) What new observations could you make that would prove or disprove the existence of the differences you came up with in the previous question? 22. (1 pt) State your conclusions and relate them to your hypotheses. Astronomy Introduction to Astronomy

8 23. (3 pts) Devise your own scientific test of astrology (the idea that you can predict personalities and fates based on the positions of planets and stars). Clearly define the methods you would use in your test and how you would evaluate the results. OR Science is useful in many aspects of everyday life. Think of a problem or question you encounter in day to day life that you might be able to solve using the scientific method. What is your hypothesis/model? What testable predictions does it make? Astronomy Introduction to Astronomy