Assignment 2 – Statistical Methods(MATH 1068) SP2 2021Instructions• This assignment is worth 20% of your final grade and is due at 5pm Friday 4th of June.• Submission is online and through the Learnonline website only.• Assignments will be marked and returned online.• Minitab output will be required in some sections, to avoid losing any information whenuploaded. The file submitted should be a PDF document.• The marks for each question is displayed next to the question.• It is important that you follow any instructions or guidance in the questions, such as “UseMinitab” where required.• The assignment consists of a total of 75 marks.• Any late submission will attract a penalty of 10% off the maximum marks available perday. The cut-off time is 5pm each day.Question 1 (12 Marks)Wave Data: The data collected is based on a comparison study between two differentmooring methods to analyse the amount of electricity generated from using waves at sea.The difference between the two mooring methods is the effect of the bending stress in partof the device where Method 1 had cheaper components in the system. Both methods wereapplied to the same subjects and where the sample sea states are the same. The question ofinterest is whether the bending stress differs for the two mooring methods.You will need the MINITAB worksheet called waves.MTW for this question, which you candownload from the Data files folder within the course website.For full marks, ensure that appropriate axis labels and meaningful titles are included withall your graphical displays for this question.(a) (2 marks) Set up the null and alternative hypotheses for this problem.(b) (2 marks) Use MINITAB to calculate the sample mean, sample standard deviation andtest for Normality.(c) (8 marks) Statistically test at a 10% level of significance whether the two mooringmethods are significantly different. Include a conclusion in your answer. Allcalculations should be done without using MINITAB and a diagram included.Question 2 (32 Marks)Ore Data: In a study to investigate the concentrations of copper in ore, the following data inthe dataset ore.MTW was collected. It represents three independent locations, the averagesize per mining site and the Copper Concentration (kgs). If there is a higher CopperConcentration, then this physically translates to the site being older and richer in minerals.(a) (8 marks) A mining company claims that for a site to be financially viable then theCooper Concentration level at sites should be above 60. At the 5% level of significance,test whether the average copper concentration is above 60 kgs.(b) (10 marks) Check the assumptions for ANOVA and test at the 5% significance level todetermine whether there is a difference in Copper Concentration between thedifferent regions. Include the post-hoc Tukey test to identify which pairs are different,if appropriate. Include your MINITAB output for full marks.(c) (3 marks) By examining the patterns in the data, make a recommendation aboutwhich regions have higher Copper concentrations. Summarise the results of youranalyses from parts (a) to (c) (3-4 sentences).(d) (8 marks) By using the table of counts in the ore.MTW dataset, conduct an appropriatehypothesis test to determine whether the Site Area is related to the Region at a 5%level of significance.(e) (3 marks) What conclusions can be drawn from the residuals in the table? State all thesignificant residuals in the answer.Question 3 (31 Marks)World Health Data: The dataset healthUS.MTW contains data from US Department of Healthand Human Services, National Centre for health Statistics and 3rd National Health & NutritionExamination Survey. The data contains numerical variables which are BMI (Kg/𝑚!), Age(years), Height (cm), Weight (kg), Cholesterol (mg) and Waist (cm). It is important to analysethe data, make predications and draw conclusions on the association between the variousvariables.You will need the MINITAB worksheet called healthUS.MTW for this question, which you candownload from the Data files folder within the course website.For full marks, ensure that appropriate axis labels and meaningful titles are included withall your graphical displays for this question.(a) (4 marks) Use Minitab to compute the correlation coefficients for BMI (kg/𝑚!) witheach other variable. Discuss each case, providing the value for the correlationcoefficient and an interpretation of the value. What is the best predicator variable toanalyse BMI (kg/𝑚!) and why? Why would you not choose Weight (kg) to predict BMI?(b) (2 marks) Use Minitab to produce a scatterplot for BMI (kg/m^2) versus your bestpredicator variable from part (a). Describe the relationship observed from the display.(c) (6 marks) Run a linear regression model in MINITAB. Are the requirements for a linearregression model satisfied? The requirements to verify are Linearity, Independence,Normality and Population standard deviations. For full marks attach your MINITABoutput.(d) (2 marks) What is the value of the intercept and is the value significant? Is theintercept meaningful?(e) (3 marks) What is the value of the slope? What does the slope measure in thisscenario?(f) (3 marks) What is the value of the coefficient of determination? What precisely doesit measure in this example?(g) (6 marks) The regression model from the MINITAB output predicts the BMI given yourchoice of predictor variable. Calculate the average of your predicator variable and usethe regression model for this value to predict their BMI (kg/𝑚!) on average? Is thisprediction accurate? Give reasons.(h) (5 marks) Based on your answer from part (g), use MINITAB to calculate the 95%prediction interval and the margin of error for the predicted value in (g). State theformula for the 95% prediction interval and interpret the meaning of the margin oferror. Full marks attach your MINITAB output.
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