A student measured the data in the tables below by recording the time, t, it took two different cylinders (one solid and one hollow) with the same dimensions to roll, from rest, down a slope for a fixed distance.
Theory suggests that the hollow cylinder should take longer to travel the same distance as the solid cylinder. Hollow Cylinder times, t/s Solid Cylinder times, t/s 2.08 2.03 1.88 1.88 2.07 2.07 1.79 1.87 2.05 2.01 1.80 1.90 2.04 2.16 1.85 1.78 2.03 2.03 1.90 1.81 2.12 2.01 1.76 1.74 2.06 2.05 1.62 1.73 2.07 2.08 1.72 1.79 1.97 2.11 1.77 1.87 1.99 2.12 1.77 1.82 2.10 2.00 1.81 1.79 2.06 2.01 1.77 1.84 2.07 2.02 1.81 1.83 2.06 1.99 1.84 1.77 2.13 2.07 1.86 1.80 1.98 2.10 1.80 1.73 2.04 2.02 1.78 1.77 2.05 2.11 1.76 1.84 2.03 2.08 1.82 1.95 2.02 2.08 1.81 1.87 2.00 2.07 1.67 1.79 1.97 2.12 1.84 1.89 2.10 2.03 1.74 1.87
To analyse the data it is suggested to the student that she groups the data and produces a histogram for each cylinder showing the distribution of rolling times. The student consults her lecturer who suggests the following class intervals, where t is the rolling time in seconds: A B C 1.50
a.The student decides to use the class intervals shown in column C in the table, explain why this is an appropriate choice for the data from this experiment.
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Construct histograms for the experimental data using the class intervals shown in column C of the table above.
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Calculate the mean rolling time for each of the cylinders.
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Produce a spreadsheet to calculate the standard deviation in the rolling time for each cylinder – the spreadsheet table should show the additional columns required and a print out including the formulae you have used in each cell is required.
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Use the “Comparison of Means Test” (Shown below) to determine whether there is significant difference in the rolling time between the two cylinders.
Comparison of means test (i) Calculate the difference between the mean values of each data set.
(ii) Calculate the “Standard error of the difference” using the formula below:
Standard error of difference = √((S1/n1)+ ) (S2/n2) (the frist one is S1 2 and next is S2 2 )
Where: s1 is the standard deviation of data set 1, n1 is the number of measurements in data set 1, s2 is the standard deviation of data set 2 and n2 is the number of measurements in data set 2.
If the difference between the mean values of each data set is greater than twice the standard error of the difference then you can be 95% confident that there is a significant difference between the two sets of data i.e. whatever has been changed between one data set and the other has influenced the results.
