Assignment 1-S1-2018 Semester 1, 2018 Page 1 of 3 STA1010 Statistical Methods for Science ASSIGNMENT 1 DUE DATE: to be submitted by NOON MONDAY 9th April, 2018. The completed assignment should be...

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Assignment 1-S1-2018 Semester 1, 2018 Page 1 of 3 STA1010 Statistical Methods for Science ASSIGNMENT 1 DUE DATE: to be submitted by NOON MONDAY 9th April, 2018. The completed assignment should be placed in your tutor’s submission box on the ground floor (behind lifts) of Building Rnf 9. This assignment counts towards 7.5% of the assessment in this unit. It is meant to be individual work and should be accompanied by a signed coversheet. Access to MS Excel is needed for some questions. Your work should be presented in a neat and readable manner. Total marks = 50 Question 1 [10 Marks] In lectures we discussed a case study in which researchers investigated whether hair grows back thicker after shaving (see http://www.scientificamerican.com/article/fact- or-fiction-if-you-shave-or-wax-your-hair-will-come-back-thicker/). a) Design a study to investigate this question using our STA1010 class as a sample. Assume the class has 200 students: 100 male and 100 female. Describe the experiment and illustrate using a schematic diagram. Treat males and females separately. b) What is the population being sampled? What type of sampling is this? Discuss whether the sample is representative of this population. c) Comment on aspects of control, randomisation, replication and blocking. d) Say what comparisons you would make at the end of the experiment. Question 2 [7 Marks] Retrieve the Excel file pulse.xls from moodle / Clayton Campus Lab Resources / Excel Folder. a) State the five-number summary for the weight of males. b) State the five-number summary for the weight of females. c) Draw comparative boxplots of the weights of males and females in the class. d) Find the 10th and 90th percentiles of female weights. How many standard deviations are the values from the mean female weight? Question 3 [6 Marks] A study was made of the excuses given by students for handing in work late in 3 countries. The numbers in each category were as follows: EXCUSE SICK RELATIVE CAR PROBLEM ANIMAL TRAUMA CRIME VICTIM AUSTRALIA 16 5 1 8 COUNTRY U.S. 20 17 2 21 FRANCE 4 8 17 1 (a) Find the marginal distribution for Excuse. STA1010 Statistical Methods for Science Page 2 of 3 (b) Find the conditional distribution for Excuse given the student came from France. (c) Do the data suggest Excuse and Country are independent? Explain. Question 4 [8 Marks] In a remote tropical region, there is a direct road from A to B but it is impassable about 50% of the time due to rain. An alternative route passes through a third location C. Suppose the road from A to C is passable 75% of the time, while the road from C to B is passable 70% of the time. Also, from past experience, if the road from A to C is passable, then the road from C to B is passable 80% of the time, and if the route from A to C to B is passable, then the direct route from A to B also has an 80% chance of being passable. a) State the information given in the question in probability notation. b) What is the probability a traveller can get from A to B? c) A traveller journeys from A to C and stays overnight. During the night, rain makes the road from A to C impassable. What is the probability the traveller can still get from C to B? Question 5 [11 Marks] In 1981, n = 78 bluegills were randomly sampled from Lake Mary in Minnesota. The researchers (Cook and Weisberg, 1999) measured and recorded the age in years and the length in mm of each fish. These data are available in the file bluegills.txt provided with this assignment on moodle. a) Identify the explanatory and response variables in this data set. b) Use Excel to perform a simple linear regression for these data. Present Excel output as part of your answer and state the linear model that it infers. c) Use Excel to fit a quadratic model of the form ŷi = β0 +β1xi +β2xi 2 to these data. Present Excel output as part of your answer and state the linear model that it infers. d) Produce a scatterplot of the data and curves representing both of the above models. e) Which of these two models is more appropriate for these data? Present and discuss residual plots and AIC calculations as part of your answer. Question 6 [8 Marks] A magician performs the following card trick. She asks a volunteer to secretly select a number between 1 and 10 and deal out that many cards from a well-shuffled deck of 52 standard playing cards. The last card dealt determines a new number of cards to be dealt from those remaining: if it is an ace, the new number is 1; if it is Jack, Queen or King, the new number is 5; otherwise the new number is the face value of the card. The process is repeated until there are not enough cards left in the deck to continue. The magician then identifies the last card selected. Semester 1, 2018 Page 3 of 3 The trick is that the magician repeats the process starting with the number 1. This will usually (but not always) result in selecting the correct final card, no matter what number the volunteer originally selected. a) Perform an experiment to estimate the probability the magician and the volunteer end up with the same final card. Give full details of the experiment and result. You may pool results with other students. (Keep your results – you will need them again for Assignment 2!) b) What is the population you are sampling in this experiment? c) Explain why the magician and volunteer are likely to end up with the same card, no matter what number the volunteer chooses initially. (End of assignment)