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Timed Online Assignment
Methods of Data Analysis: Exploring
Thursday, 21 May 2020 7:30 pm – 10:00 pm
Time allowed: 2.5 hours
INSTRUCTIONS TO STUDENTS: 1. This Timed Online Assignment contains THREE (3) questions. 2. You must answer ALL questions. 3. If you have any queries about a question, or believe there is an error in the question, while the assignment is in session, briefly explain your understanding of and assumptions about that question before attempting it. 4. Upon completion of your assignment, submit it online via Canvas (similar to Tutor Marked Assignment (TMA) submission). 5. Your submission should consist of only one file and of no more than 500MB in size. 6. Please submit your answers at the end time of your assignment. Thereafter, you will not be able to submit your answers and you will be considered as having withdrawn from the course. No appeal will be allowed. 7. To prevent plagiarism and collusion, your submission will be reviewed by Turnitin. The Turnitin report will only be made available to the markers and you will not be able to view it after the submission deadline. 8. The University takes plagiarism and collusion seriously, and your Turnitin report will be examined thoroughly as part of the marking process. 9. To pass this assignment, you are required to apply relevant theories and concepts, and not merely cite or copy content from your reference materials.
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Answer ALL questions.
Question 1 (40 marks) A group of researchers have come up with a new and improved method to measure the size of brains in people while they are still alive. Through a recruitment drive online and in the newspapers, they managed to recruit forty participants who consented to having their brains measured. The following is a screenshot of the descriptive statistics of the data collected. a) Examine the descriptive statistics presented above and draw at least two types of frequency distribution graphs that may represent the data. Explain your answer. (10 marks)
Page 3 of 6 b) The researchers managed to measure the brain size of one additional participant. The brain size of this new participant is 1830cm3. Apply the necessary formula to calculate the new sample mean and standard deviation including the data from this new participant and draw a frequency distribution graph that best describes the new set of data. Show all necessary calculations. The variance of data from the original forty participants calculated using the new mean is 11961.3. You may use this new variance and any of the formula below to help you answer Question 1b. (20 marks) c) After calculating the new sample mean, the researchers conclude that the new sample mean represents the average brain size of the human race. Examine the appropriateness of this conclusion and explain why the conclusion is appropriate or inappropriate. (10 marks)
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Question 2 (35 marks) Researcher X is interested in understanding whether regularly commuting by bus or train affects how tired commuters feel. He suspects that regular bus commuters will feel more tired compared to regular train commuters. He recruited 2,000 participants from bus interchanges and train stations around the island and asked if they take either the bus or train to work regularly. He asked a dozen additional questions on their general perceptions of how tired they feel on a slider scale ranging from 0 being not tired at all to 100 being the most tired they have been. This is a measure that is often treated as having an interval scale level property. He then ran some analyses to answer his research question. a) Formulate the most appropriate null and alternative hypotheses for the analysis that Researcher X is running. (5 marks) b) Researcher X compares the bus and train commuters on each of the twelve different questions he collected on their perception of tiredness. The following is the output from the analysis that Researcher X felt was most promising. Interpret the results of the analysis, and evaluate if Researcher X’s hypothesis is supported and report them in APA format. You may use any of the formulas below to help you answer the question. (15 marks)
Page 5 of 6 c) After looking at the results, Researcher X claimed that taking buses to work caused commuters to be tired and that the effect is strong because of statistical significance with a very small p value. Examine why his claim is inappropriate by identifying at least three issues with the study and analyses. (15 marks)
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Question 3 (25 marks) Mr P, a human factors engineer, is investigating how arousal, whether someone is aroused or relaxed, affects the number of mistakes made during a complex psychomotor task. He randomly assigns 180 participants equally into two groups, with one group receiving a stimulant before going through the task, and another group receiving a relaxant before going through the task. He then measures how many mistakes each participant makes while doing the task. After collecting the data, he is advised by his boss to run a one-way between-subjects ANOVA to analyse the data. a) Would you recommend a one-way between-subjects ANOVA as an appropriate statistical test for analysing the data? Explain your answer. (5 marks) b) Examine the results prepared by Mr P after he ran the analyses and identify any issues with the results and/or reporting. We found that participants who received the relaxant made more mistakes (M = 3.92, SD = 0.85) compared to participants who received the stimulant (M = 3.88, SD = 0.91) and this difference is statistically significant, F(1, 175) = 0.04, p < .05, η2 = 0.0002. (5 marks) c) The actual relationship between arousal and mistakes made are shown in the figure below with negative values of arousal indicating a more relaxed state. Imagine that there were three engineers who conducted studies independently. One engineer was range-restricted to participants in the more relaxed end of the spectrum, one engineer was range-restricted to the more aroused end of the spectrum and the last engineer did not encounter range restrictions. Interpret the graph and explain whether these three engineers will have similar or dissimilar conclusions at the end of their studies. (15 marks)
—– END OF PAPER —–
Given the nonharmonic forcing function applied to a 1-DOF mass-spring-damper system:
The response (particular solution) is:
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