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Queensland University of Technology Science and Engineering Faculty School of Mathematical Sciences MXB107 – Statistical Models for Data: Relationship and Effects Assignment #3 – Semester 2 2016 – SOLUTIONS Please submit your answers using the TurnItIn tool on the MXB107 Blackboard site by 11:59pm on Friday 7th October 2016. Light Speed: The physicists Albert Michelson and Edward Morley are renowned for their joint work on measuring the speed of light and demonstrating that it is a universal constant. During June 1879 on each of 5 different days they each undertook 10 repetitions of an experiment designed to measure the speed of light. For each experiment they recorded the speed of light in km/msec. The current accepted speed of light is 299.7345 km/msec. The data from 5 days × 10 repetitions × 2 experimenters = 100 experiments if given in the file speedOfLight.csv. The file consists of 4 columns: • Date assess H0: 𝑝𝐷𝑎𝑦1 = 𝑝𝐷𝑎𝑦2𝑡𝑜5 is (0.7 – 0.45)/�0.5(1 − 0.5)((1/20) + (1/80) = 2 (+1/2). Thus the p-value is Pr(|N(0 1)|>2) = 0.0455 and we do not reject the null hypothesis (+1/2) BONUS: A measurement from the 100 experiments is randomly selected and turns out to be greater than 0.85. What is the probability that it is from Day 1? ANSWER: Pr(>0.85|Day 1) = 0.7 Pr(>0.85|Day 2 to 5) = 0.45 and Pr(Day 1) = 1/5 = 0.2. So by Bayes’ rule we have Pr(Day 1|>0.85) = Pr(>0.85|Day 1)Pr(Day 1)/ {Pr(>0.85|Day 1)Pr(Day 1) + Pr(>0.85|Day 2 to 5)Pr(Day 2 to 5)} = 0.7(0.2)/{0.7(0.2) + 0.45(0.8)} = 0.28 Alternatively we can just note that there are 50 observations larger than 0.85 and 14 come from Day 1 so the probability is 14/50 = 0.28. (+1 for either approach) MXB107 Semester 2 2016 Assignment 3 SOLUTIONS Page 3 out of 3 [...]

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Light Speed: The physicists Albert Michelson and Edward Morley are renowned for their joint work on measuring the speed of light and demonstrating that it is a universal constant.

Subject Area: Mathematics

Document Type: Dissertation Proposal