1015SCG Workshop Week 4

1015SCG Quantitative Reasoning Week 4 Workshop 1. Find the value of c and the error if x = 2 ± 0.1 , y = 3 ± 0.05 . Make sure that the value and the error are properly rounded. a. c = 3 ∗ x b. c = x + y c. c = x − y d. c = x ∗ y e. c = x y f. c = x 3 g. c = √ y h. [Harder] c = √ x 2 y 2. The following counts were made of distinct possum sightings in Toohey Forest, over a period before Powerful Owls were observed in the forest, and then over a period after . For each of the data sets calculate: a. the mean, b. the standard deviation, c. the standard error in the mean, d. discuss the result, can you say that the population of the possums was affected by the owls? Hint: Use Excel functions. Possum Sightings: Before Powerful Owls 52 38 62 66 44 41 46 After Powerful Owls 20 31 40 19 20 41 44 25 3. We will investigate whether a given coin is fair (i.e. has a 50% of landing Heads of Tails) a. Toss a coin 10 times, and record the number of Tails that land. b. Make up a table containing your results, and add results from other students in your workshop 1 . Hint: instead of tossing the coin you can use an Excel function =randbetween(0,1) Fraction of coin tosses landing Tails: My attempt Others’ attempts 1 2 3 4 5 6 7 8 9 10 /10 /10 /10 /10 /10 /10 /10 /10 /10 /10 c. From your table, calculate the average and standard error. d. Does the expected answer (50%) lie within your margin of error? 4. Calculations involving error propagation. a. The age of the universe is reported as 13.80 ± 0.02 billion years. What is the age of the universe (with error) in minutes? b. I have a solution of 2 ± 0.01 mmol/l of methanol. What is the concentration (with error) in g/l? c. If I add 2 ± 0.05 ml of methanol to 98 ± 0.1 ml of water, i. how much liquid in total (with error) do I have? 1 If you miss the workshop, then repeat the experiment as many times as your patience permits!