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Assignment 1 2023

Assignment 1 is due no later than 11:59pm Friday 8th of December, 2023. You must submit your assignment electronically as a single file (only pdfor Word) via the LMS page for this subject. Where appropriate, your solutions must include your workings.

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 5 marks for completeness (you will only get the full 5 marks for completeness if you make a serious attempt to answer every question) and a further 5 marks for your written communication (e.g. clarity, spelling, grammar, correct use of notations etc.): 40 + 5 + 5 = 50 marks.

1. A survey was conducted at La Trobe University and a selection of questions based on those asked in the survey are presented below.

1. What is your blood type (e.g., A, B, AB, O)?

2. Do you have a car?

3. What is temprature today in Celsius?

For a randomly selected individual, let

❼ X denote their response to Question 1,

❼ Y denote their response to Question 2 and

❼ Z denote their response to Question 3.

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. E.g. if you believe statements A and B are both correct, you should report both.

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. X 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 quantitative variables.

F. X is a categorical variable and Z is a quantitative variable.

G. None of the above statements are correct. (3 marks)

2. Extremely large numbers can be difficult to write down. When doing so, we can make our task much easier by using scientific notation (or exponential notation).

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.

Using this information, complete the following questions.

(a) Fifty decillion is equal to

50, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000.

Write down this number using scientific notation. (3 marks)

(b) Now, enter the number in part (a) in its long form (i.e. the ‘5’ 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. (3 marks)

(c) The (approximate) minimum number of ants on Earth can be written as 2000 followed by 13 zeroes. Write down this number using scientific notation. (3 marks)

(d) There exists a number x such that x!, i.e. x factorial, is reasonably close to the number given in part (c). For this question you will need to use 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.	16!
B.	17!
C.	18!
D.	19!
E.	20!
F.	21!

(5 marks)

3. In the Week 1 lectures we briefly mentioned 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 ✗ to indicate that the person is not a ‘yes’ for any of these questions (e.g. did not die at the age of 27 years).

Name	Died at 27? Was a famous musician or actor?	A member of the 27 club?
Amy Winehouse
Pat Tillman
Ahmed I
Buddy Holly
Lucky Luciano
Ukyou Kamimura (Kami)
Bobby Sands

(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

considered good?

Ranks

Slovenia

Israel

Spain

Portugal

Income inequality

Unemployment rate

Level of Democracy

Gallup Global Wellbeing Index

Food Insecurity

Life Expectancy at Birth

Prison Population (per 100,000)

Math Scale Score

Science Scale Score

High

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 Slovenia, Israel, Spain and Portugal. 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. Spain received the number 1 rank because, of the four countries we are 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 Slovenia we will add up all of the ranks in the column denoted ‘Slovenia’ to obtain a single total sum ofranks. Do this for each country and

provide the totals below (write the number above ......... as appropriate for each country):

Total sum of ranks for Slovenia = .........

Total sum of ranks for Israel = .........

Total sum of ranks for Spain = .........

Total sum of ranks for Portugal = .........

(4 marks comprised of 1 mark for each correct total rank)

(d) Now use the total sum ofranks 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 the the total sum of ranks above agree with the ordering of nations provided in Table 2? Explain (2 marks)

5. Complete the Academic Integrity quiz located under the Assignment 1 folder in the Assessments section of LMS. This quiz considers a scenario designed to help us think through issues relating to Academic Integrity. Although you will get a score for completing this quiz, your actual score is not important and will not be graded/assessed. What is important is that you engage in this activity and give thought to some of the tricky issues arising from it. One mark is awarded for completeness if all questions on the Academic Integrity quiz have been completed. (This question carries no marks for accuracy or written communication.)