Data Collection Concept - Assignment Example

Data Gathering and Analysis Assignment Task 15 Marks) Any measuring device that makes an indirect measurement to come up with a supposedly accurate answer relies on calibration for accuracy. For example, an electronic laboratory balance measures changes in electrical resistance in “load cells” and is calibrated to correlate particular resistance measurements with the weight that caused the changes. Your task is to select or create an appropriate measurement device and produce a formula that will enable that device to make accurate (or more accurate) measurements. Make a series of measurements (preferably at least 20 if possible) against accurately known standards. You can either use the raw data (like the balance resistance measurements, if you can get at them) or the measurement the device produces (like the weight shown on the balance display). If you use the measurements the device produces, it would be best if you use a device that you suspect is not giving very accurate measurements, and your formula will enable you to improve its accuracy. (10 marks) Graph the measurements against the standards and determine a formula that would best enable you to make accurate measurements or correct the answers the device gives. Log transform the data if necessary. Raw Data The data was obtained from readings given by a weighing device from standard weights. The data is shown below. Actual (Standard) weight (g) Observed weight 5 4.95 10 10 20 20.07 50 51.03 100 98.78 200 200.07 250 250 300 302.72 500 499.8 600 601.44 700 700.91 750 749.3 800 800.9 1000 1003.2 1500 1503 2000 1997.45 3000 3004.76 4000 4002 5000 5004.54 10000 10006 Bar graph for standard measures and observed weights We use regression method to come up with a formula to determine the true weights. The summary for the output is shown below: SUMMARY OUTPUT   Coefficients Standard Error Intercept 0.336617 0.426063 X Variable 1 1.000623 0.000151 Real weight = 0.336617 + 1.000623 (Observed weight) (4 marks) Replace X and Y in your formula with the appropriate words X = Standard weight Y = Observed weight (1 mark) Use one worked example to show how your formula can be used. To obtain the real weight for an observed weight of 348.94g: Actual weight = 0.336617 + 1.000623 (Observed weight) Actual weight = 0.336617 + 1.000623 (349.94) = 350.49g (1 mark) Convert your formula so that you can predict what result the device will give with one unknown standard from within the data range (interpolation) and one standard outside the data range (extrapolation) is measured. Test to see if your prediction was correct. Comment on the result of this exercise. Observed weight (which will be given by device) = (Actual weight – 0.336617) / 1.000623 To test the formula, we test using a 10000g standard weight. Observed weight for 10000g standard weight is given by: = (10000 – 0.336617) / 1.000623 = 9993.44 This exercise shows that measures obtained from measuring devices must be subjected to corrective methods. Besides, measuring devices must be calibrated on a regular basis to reduce instances of error. (4 marks) Task 2 (10 Marks) Produce a graph showing the Olympic Games gold medal times for the men’s 100 metre sprint event from as far back as you can find to 2012. Use the Excel Chart Labeler Add-In to enter the names of the athletes on the graph. (6 marks) Predict the winning time for the 2016 and 2020 Olympic Games. (Last year’s students predicted a time of 9.65 seconds. How close were they?) SUMMARY OUTPUT   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 36.31048 2.471928 14.68913 4.2E-14 31.22936 41.3916 X Variable 1 -0.01326 0.001265 -10.4889 7.78E-11 -0.01586 -0.01066 The predicted winning time for the 2016 and 2020 Olympic Games can be obtained through regression or by interpolating the straight line (line of best fit) through the curve: 1. Using the regression equation, the predicted winning time for Olympics is obtained as follows: Equation: Y = a + bX, where X = year of interest, Y = record time From the output shown above, the equation is given as Y = 36.31 – 0.01326X Hence, 2016 record time = 36.31048 – 0.01326(2016) = 9.58s Similarly, 2020 record time = 36.31048 – 0.01326(2020) = 9.52s 2. Using interpolation, 2016 record time = 9.58s Similarly, 2020 record time = 9.52s The two methods give similar record times. (2 marks) Also determine the year at which Olympic Games an athlete is likely to break the 9.5 second mark. Demonstrate how you have tried to make these predictions as accurately as possible, and explain how you knew which was the most accurate method. To determine the year at which Olympic Games an athlete is likely to break the 9.5 second mark, the regression equation is employed: Y = 36.31 – 0.01326X, but Y = 9.50; 0.01326X = 9.5 – 36.31048 X = -26.81048 / -0.01326 X= 2022. Hence, the year at which Olympic Games an athlete is likely to break the 9.5 second mark is 2022. Task 3 (15 Marks) Follow the Pivot Table notes in the Two Sample Tests Exercise document. Complete the exercises if you haven’t already done so. This will prepare you to be able to complete this exercise, which uses the same database. From the data in this spread-sheet (the pulse project database) from students at the Univ of Queensland (UQ), Bay of Plenty Polytech (BP) and Wintec (WT), answer this question as allocated: Do smokers tend to be older or younger than non-smokers? Use a pivot table to summarise the data relevant to your question. Smokes Count of Age Sum of Age Average of Age NonSmoker 116 2439 21.02586207 Smoker 14 297 21.21428571 Grand Total 130 2736 21.04615385 (4 marks) Perform a two sample t-test to see if there is a difference between your 2 sets of data. t-Test: Two-Sample Assuming Unequal Variances Variable 1 Variable 2 Mean 21.21428571 21.02586207 Variance 10.95054945 26.99932534 Observations 14 116 Hypothesized Mean Difference 0 Df 22 t Stat 0.187032167 P(T Read More