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301114 The Nature Of Data

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In this assignment there are 3 questions (split into various parts). For each question/part you should draw appropriate plots, conduct the analysis and describe the conclusions in words. A report can be submitted as either a PDF (preferred) or Word document. It is advisable that your report includes the R-code used so that partial credit can be awarded in case of error. You can create the word/pdf file using Rmarkdown if you know how, but this is not compulsory.
Submission is due by Friday for week 12. Submission is by the vUWS online system.
1. a. The following table shows the number of prisoners in Australian prisons in 2014, broken down by age group and gender. Is there evidence that the age distribution differs by gender Make a appropriate plot of the data.
Males Females
19 years and under 920 65
20 to 24 years 4684 316
25 to 29 years 5624 475
30 to 34 years 5407 483
35 to 39 years 4609 404
40 to 44 years 3756 349
45 to 49 years 2408 234
50 to 54 years 1541 135
55 to 59 years 975 72
60 to 64 years 595 32
65 years and over 681 27

prisoners = cbind(Males = c(920, 4684, 5624, 5407, 4609, 3756, 2408, 1541, 975, 595, 681),
Females= c(65, 316, 475, 483, 404, 349, 234, 135, 72, 32, 27))
rownames(prisoners) = c("19 years and under", "20 to 24 years", "25 to 29 years",
"30 to 34 years", "35 to 39 years", "40 to 44 years",
"45 to 49 years", "50 to 54 years", "55 to 59 years",
"60 to 64 years", "65 years and over")

b. Data has been collected on the number of car insurance claims in two areas of Sweden, Stockholm and surrounds and rural southern Sweden. In Stockholm there were 23174 claims from 326149 policies, whereas in the rural area there were 31913 claims from 846957 policies. Is there evidence that the rate of car insurance claims is different in the two areas
2. The file PIMA.csv contains information about the Pima people from North America. A number of social and environmental factors have contributed to them having one of the highest rates of type 2 diabetes in the world. This data set contains information of around 700 female individuals, including • ever.pregnant — Whether the individual has ever been pregnant
• diastolic — diastolic blood pressure
• bmi — Body Mass Index
• age — age in years

Is there evidence that body mass index differs for women who have had a pregnancy versus those that haven’t In what direction is any difference Make an appropriate plot of the data.
3. a. Diastolic blood pressure is thought to vary by age. Make an appropriate plot of the data. Compute a 95% confidence interval for the Pearson correlation of age and diastolic blood pressure in female Pima people.
b. Fit the simple linear regression of diastolic and age. Interpret the slope of the regression. Compute a 95% confidence interval for the mean diastolic blood pressure of a 40 year old female of the Pima people.
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