its about Data-based critical thinking subject
STA1DCT Assignment 1 Assignment 1 is due no later than 5pm Thursday 19th of March, 2020. You must submit your assignment electronically and as a single file (only pdf or Word) via the LMS page for this subject. Where appropriate, your solutions must include your workings. In submitting your work, you are consenting that it may be copied and transmitted by the University for the detection of plagiarism. Please start with the following statement of originality, which must be included near the top of your submitted assignment: “This is my own work. I have not copied any of it from anyone else.” IMPORTANT NOTE: The total possible marks for this assignment is 50. There are 40 marks associated with accuracy (i.e. correctness of your answers; the breakdown of these marks is indicated on this question sheet), a further five marks for completeness (you will only get the full five marks for completeness if you make a serious attempt to answer every question) and a further five marks for your written communication (e.g. clarity, spelling, grammar, correct use of notations etc.) STA1DCT: 40 + 5 + 5 = 50 marks. 1. The last Australian Household Census was held on the 9th of August, 2016. Below are snapshots of questions taken from the Census Form. The number to the left of the question is the question number as it appeared in the form. 7. Is the person of Aboriginal or Torres Strait Islander origin? 24. Is the person attending a school or any other educational institution? 32. For each female, how many babies has she ever given birth to? For a randomly selected individual, let X denote the response to Question 7, Y denote the response to Question 24 and Z denote the response to Question 32. Consider the below statements, each identified by a letter (i.e. ‘A’, ‘B’ etc.) To successfully answer this question, provide the letter(s) identifying ALL correct statements. You will get zero marks for this question if you (i) do not identify all of the correct statements or (ii) include a statement that is incorrect. A. Y is a quantitative variable. B. Z is a categorical variable. C. X and Y are both categorical variables. D. Y and Z are both quantitative variables. E. X, Y and Z are all categorical variables. F. X is a categorical variable and Z is a quantitative variable. G. None of the above statements are correct. (2 marks) 2. Very big numbers can be difficult to write down. However, using scientific notation (or exponential notation) can make this much easier. Let us consider a simple example. Note that 102 = 10×10 = 100 and 7×100 = 700. Therefore we can write 700 = 7 × 100 = 7 × 102. Writing 700 as 7× 102 is known as writing 700 using scientific notation. Similarly, we can write 3, 000 = 3× 103 and 3, 500 = 3.5 × 103. Now, complete the following questions on the next page. 1 (a) Nine hundred septillion is equal to 900, 000, 000, 000, 000, 000, 000, 000, 000. Write down this number using scientific notation. (2 marks) (b) Now, enter the number in part (a) in its long form (i.e. the ‘9’ followed by all the zeroes) into an empty Excel worksheet cell and hit ENTER. Write down exactly what is now stored in that cell (this is how Excel represents numbers using scientific notation). NOTE: To ensure that you will be provided with the number you have entered in scientific form (that is, displayed using scientific notation) do the following (i) right-click, using the mouse, on the cell you entered the number into (ii) select Format Cells... (iii) then click on the Number tab, select Scientific and press OK. (2 marks) (c) The number of water molecules in a single drop of water can be written down as the number 2 followed by 18 zeroes. Write down this number using scientific notation. (1 mark) (d) There exists a number x such that x! is reasonably close to the number given in part (c). For this question you will need Excel to work out some factorials that equate to extremely large numbers (look up how to do this either on the internet or via some other source). You will also need to be able to understand how Excel represents numbers using scientific notation (e.g. see part (b) above). Which of the following choices below is the closest to the number given in part (c)? To answer this, simply circle the letter corresponding to the best answer. A. 18! B. 19! C. 20! D. 21! (4 marks) 3. In the Week 1 lectures we considered the 27 club which includes famous musicians who died at the age of 27. More information and a list of at least some members can be found at the website http://en.wikipedia.org/ wiki/27_Club. In recent times inclusion into the 27 club has been broadened to include famous actors. To answer this question, please complete the empty cells of the table below (at least a table that resembles this table in your submission). There is one line for each famous name and the first one, Amy Winehouse, has been completed for you. For example, Amy was a famous musician so she gets a under the question ‘Was a famous musician or actor? ’. She was also 27 when she died so she also gets a for the second question. Now, because she was both a famous musician and was 27 when she died, she is also a member of the 27 club hence the reason for the for the final question. When completing the rest of the table, use an 7to indicate that the person is not a ‘yes’ for any of these questions (e.g. did not die at the age of 27 years). 2 http://en.wikipedia.org/wiki/27_Club http://en.wikipedia.org/wiki/27_Club Name Died at 27? Was a famous musician or actor? A member of the 27 club? Amy Winehouse Elvis Presley Tom Pryce Leonard Siffleet Nero Claudius Drusus Prince Rogers Nelson Peter William Ham (6 marks; 1 mark for each correct line (not including the line for Amy Winehouse)) 4. On February 18, 2011 the New York Times published an opinion piece called Empire at the End of Deca- dence1 which was critical of the current state of affairs in the United States. Also included was an interesting table which is provided as Table 2 which is at the end of these question sheets. This table provides many indices that may used to gauge the overall ‘well being’ or performance of a nation (only some nations are represented). The actual table has a color coding where a dark red shade indicates that a nation is performing poorly according to the associated index. The table ranks countries in order from best to worst where Australia is ranked the best and the United States is ranked the worst. You can find the full color graphic on LMS. Index Are High or Low values Ranks considered good? Germany Switzerland Denmark Japan Income inequality Unemployment rate Level of Democracy Gallup Global Wellbeing Index Food Insecurity Life Expectancy at Birth High 3 2 4 1 Prison Population (per 100,000) Math Scale Score Science Scale Score Table 1: Table to completed as part of Question 4. For this question, for simplicity we will consider only four countries listed in Table 2 which are Germany, Switzerland, Denmark and Japan. For parts of this question you will need to fill in the empty spaces of Table 1. (a) Using the shadings as a guide, determine whether a high or low value for a particular index is considered good and write this down in the appropriate position in Table 1. For example, a high value for Life Expectancy at Birth is considered good. This has been noted for you in the table and to complete this question you need to do this for the remaining indices. (3 marks all correct; 2 marks for 1 or 2 incorrect; 1 mark for 3 or 4 incorrect; 0 marks otherwise) (b) We will now rank the four countries from 1st to 4th for each index based on the value recorded for that index. A country will receive the number 1 rank if it scored the best for that index. The number 2 rank if it scored the second best and so on. If two countries have the same index value, then we will give both the average of the two associated ranks. For example, suppose that two countries tie for first place. then the top two ranks should be given to these countries. To do this, we will give them both the number (1 + 2)/2 = 1.5 rank. Similarly, if two countries tie for second and third, then they will both receive a rank of (2 + 3)/2 = 2.5 and so on. To get you started the ranks for the Life Expectancy at Birth index are already in the table. Japan received the number 1 rank because, of the four countries we are 1See http://www.nytimes.com/2011/02/19/opinion/19blow.html 3 considering, it had the highest value and we have indicated that high values are good for this index. Now complete Table 1 for the remaining indices. (8 marks comprised of 1 mark for each correct line of ranks) (c) We will now add up all of the ranks for each country. For example, for Germany we will add up all of the ranks in the column denoted ‘Germany’ to obtain a single total sum of ranks. Do this for each country and provide the totals below (write the number above . . . . . . . . . as appropriate for each country): Total sum of ranks for Germany = . . . . . . . . . Total sum of ranks for Switzerland = . . . . . . . . . Total sum of ranks for Denmark = . . . . . . . . . Total sum of ranks for the Japan = . . . . . . . . . (4 marks comprised of 1 mark for each correct total rank) (d) Now use the total sum of ranks above to determine which country, or countries, ranks the worst overall (you must only use the numbers in part (4c) to answer this question) out of the four countries considered. Which country, or countries, is it and why? Does it agree with the ordering of nations provided in Table 2? (3 marks) 5. Without using a calculator or computer (i.e. you must derive your answer to this question by hand), show