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ACTIVITY: RANDOM SAMPLING STATISTICAL CONCEPTS: Random sample, population, sample frame, proportion, variability of a sample statistic, confidence interval for a proportion.
THE SETTING: You are the marketing representative for a local car dealership who wants to market cars to college students and faculty. By selecting a random sample, you wish to learn what characteristics of vehicles are important to this population. STEP 1: PLAN YOUR SAMPLE OF 40 VEHICLES What type of random sample do you want to take?
A. Simple Random Sample (Ex. Number spaces in one lot and pick 40 at random) B. Cluster Sample (Ex. Divide a lot or several lots into clusters by row, the select the clusters and take every space in chosen clusters)
C. Stratified Sample (Ex. Select separate samples from student vs. faculty lots)
D. Multistage Sample (Ex. Select parking lots and then select spaces in chosen lots)
Choose one of the designs above, write a sampling plan and carry it out. You should make a record of the sampling frame you use. You may want to verify your plan with your instructor before carrying it out.
THE LOCATION-You should choose the location to be a large, nearby parking lot(s). The vehicles in the lot(s) will serve as the population. It is important to keep in mind that sampling from this parking lot allows us to learn about the population of vehicles in that lot. This may or may not be representative of the entire population of vehicles driven by college students/faculty. Think about your chosen lot(s) and if it is representative of what your target population drives. Your population should be at least 10 times larger than your sample size!
STEP 2: COLLECTING THE DATA For each vehicle in a sampled parking lot space, you will choose and observe two characteristics. The characteristics you observe should be related to the vehicle’s features, such as color, # of doors, hybrid model, sedan or SUV/crossover, etc. Each characteristic needs to be phrased so you can note a “YES” or “NO” for each sampled vehicle. *Be sure to write down what specific characteristics you are going to observe. Now go to your selected parking lot(s) and based on your sample design go to each selected parking space and observe the two characteristics for the vehicle parked there. Continue sampling spaces using each successive random number until you have recorded information for 40 vehicles. Record the information in the table provided. Then summarize your data in the second table by counting up the number of “Yes” vehicles for each attribute and calculating an estimated proportion, standard error, and 95% confidence interval.
TURN THE TABLES BELOW IN AS AN APPENDIX TO YOUR REPORT. Data sheet for Vehicle Sample Vehicle Attribute 1 Yes/No? Attribute 2 Yes/No? Vehicle Attribute 1 Yes/No? Attribute 2 Yes/No?
1 21 2 22 3 23 4 24 5 25 6 26 7 27 8 28 9 29 10 30 11 31 12 32 13 33 14 34 15 35 16 36 17 37 18 38 19 39 20 40
Summary Data for Vehicle Sample Attribute Number of “Yes”
Vehicles Estimated Proportion Standard Error of the Estimate 95% Confidence Interval
WRITING ASSIGNMENT: Write a report summarizing your experiment and its findings. You should address the following issues:
1. A clear description of the population and the sampling frame, and the purpose of your sample.
2. The manner in which the sample was obtained and description of the sampling method. Include enough detail so that your sample could be repeated by a non-statistician. Discuss any pros/cons of your sampling method.
3. The data, the estimates, the intervals, and careful interpretations. Include a table of your data and at least one graph. Discuss whether or not the characteristics you observed are desired by the majority of the population (p-interval > 0.5), the minority (p-interval < 0.5), or neither (0.50 in the p-interval).
4. Conclusions and Suggestions for improved sampling procedures. Write conclusions as if you were reporting to your boss at the car dealership and making a recommendation based on your findings. Try to make connections between the two characteristics you observed. Discuss how your sampling went, i.e. if there were any practical difficulties. Grammar and spelling You may use tables to describe your results, but you should also discuss the information in paragraph form thoroughly. Don’t let a table stand by itself! There is no required length for this assignment, just as long as you need to address items 1-4 thoroughly
