Duedate:Sunday 21st May 2017 Assessmentvalue:9% • This assignment is marked out of 50 marks. Part A:Critique ofGraph [8marks] The graph below shows numbers of different types of births for New Zealand women from 2005 to 2014. It is derived from the Report on Maternity, 2014 published by the Ministry of Health. Data Source: http://www.health.govt.nz/publication/report-maternity-2014 1. Critique the above graph, discussing any strengths and weaknesses. [3 Marks] Type your answer here 2. The table below shows the data used to construct the graph above. Use this data to construct a more appropriate graph than the one above. [2Marks] Type of birth Year Spontaneous vaginal birth Assisted birth Emergency caesarean Elective caesarean Total Women giving birth 2005 38992 5190 8077 5326 57585 2006 39469 5237 8491 5960 59157 2007 42152 5570 8536 6344 62602 2008 42969 5308 8454 6493 63224 2009 42027 5420 8550 6663 62660 2010 41995 5713 8345 6865 62918 2011 40748 5350 8062 6783 60943 2012 40433 5385 8398 7146 61362 2013 37795 5129 8234 7004 58162 2014 37821 5419 8038 7050 58328 Paste your new graph here 3. Describe any trends in type of birth from 2005 to 2014. [3Marks] Type your answer here   Part B: Bears data [19 Marks] Part B of this assignment is concerned with a dataset on North American Black Bears, collected over a period of 2 years from British Columbia, Canada. The data set contains records for 100 bears in total. The data is in the spreadsheet called bears.xls 1. Exploratory data analysis [5 Marks] a) Construct a histogram of the age (in months) of bears from the dataset. (Minitab hint: Graph: Histograms: Simple) [1 Mark] Paste your graphhere b) Comment on the features of this distribution. [2 Marks] Type your answer here c) Find the mean and median for the age of bears in the dataset. Comment on any similarity or difference between them. [2 Marks] Type your answer here 2. Confidence interval [5 marks] a) Use the results above to construct and interpret a 95% confidence interval for the mean age of North American Black Bears in British Colombia. [3 Marks] Paste your Minitab output here 95% CI is: Interpretation: b) Does the shape of the histogram in 1(a) give you any concern about the validity of this confidence interval? Explain your answer. [2 Marks] Type your answer here   3. Transforming the data [5 Marks] a) Create three new columns in Minitab containing the following transformations of the ages: i. square root ii. natural log iii. reciprocal Include the first 5 rows of each column here. [1 mark] Paste your first five rows of data here b) Construct a histogram of the transformed ages for each of the three transformations. [3 marks] Paste your graphs here c) Which transformation (if any) makes the data appear approximately normally distributed? [1 mark] Type your answer here 4. Using the transformation you chose in 3c): [4 marks] a) Find the mean and median of the transformed ages. [1 mark] Mean = Median = b) Why are the sample mean and median now similar? [1 mark] Type your answer here c) Find a 95% confidence interval for the mean of the transformed data. [1 mark] Paste your Minitab output here 95% CI is: d) Back-transform your answer in c) to give an approximate 95% confidence interval for the median age of North American Black Bears in British Colombia.[1 mark] Type your answer here Part C: Hypothesis test for proportion [8 Marks] For the survival of the North American Black Bear it is important that at least 50% of bears surviving are female. 1. Whatis the proportion of American Black Bears in British Columbia that are female in the sample in the Bears.xls dataset? [1 mark] Use the information above to conduct a hypothesis test to determine if the there is cause for concern about the proportion of American Black Bears in British Columbia who are female. 2. State your null and alternative hypotheses in words and symbols. [2 marks] H0: H1: 3. Use Minitab to calculate the test statistic and corresponding p-value. [2 marks] Paste your Minitab output here Test Statistic = p-value = 4. Explain whether you have evidence against the null hypothesis or not. [2 marks] Type your answer here 5. State your conclusion in context in a form that a non-statistician would understand. [1 mark] Type your answer here Part D: Further analysis of paper plane data [15Marks] Inthis sectionyouwillusethedatayou collectedinAssignment1. • Ifyoucollectedthe datawithaclassmate,givethisperson’snameand IDnumber. (Remember that you should have different data sets and conduct separate analyses.) 1. State your research question from assignment 1 and describe your variables including their levels and units. [1 Mark] Research Question: Variables: 2. Comparing more means: ANOVA Use Minitab Express(or Minitab) to test if your numerical variable has the same true mean for the different levels of your categorical variable. a) WritedownthenullandalternativehypothesestoexaminethisquestionusingANOVA [2Marks] H0: H1: b) Use Minitab Express(or Minitab) to carryout theANOVAonyourdata [6Marks] (i) State the test statistic and corresponding p-value. Include your Minitab output. Paste your Minitab output here Test Statistic = p-value = (ii) Explain whether you have evidence against the null hypothesis or not. Type your answer here (iii) State your conclusion in a form that a non-statistician would understand. Type your answer here c) Assumption checking: [6Marks] (i) State the assumptions for the ANOVA test. Type your answer here (ii) Use Minitab Express to check whether these assumptions are valid for your data. (Hint: use Normal Probability Plots from Minitab, compare the sample standard deviations,and comment on independence). Include your Minitab output. Type your answer and paste your Minitab output and any graphs here (iii) Discuss the validity of the conclusion you made in b) (iii) (above). Type your answer here