MODULE NAME: MODULE CODE:
QUANTITATIVE TECHNIQUES B QUAT6211
QUANTITATIVE TECHNIQUES B QUAT6211p
ASSESSMENT TYPE: TAKE-HOME ASSESSMENT (PAPER ONLY)
TOTAL MARK ALLOCATION: 60 MARKS
TOTAL TIME: This assessment should take you 1 Hour to complete, however you have 21 Hours (midnight to 9PM on the same day) to submit. This additional time has been allocated to allow for the download, completion and upload of your submission.
By submitting this assessment, you acknowledge that you have read and understood all the rules as per the terms in the registration contract, in particular the assignment and assessment rules in The IIE
Assessment Strategy and Policy (IIE009), the intellectual integrity and plagiarism rules in the Intellectual Integrity Policy (IIE023), as well as any rules and regulations published in the student portal.
INSTRUCTIONS:
1. Please adhere to all instructions. These instructions are different from what is normally present, so take time to go through these carefully.
2. Independent work is required. Students are not allowed to work together on this assessment. Any contraventions of this will be handled as per disciplinary procedures in The IIE policy.
3. No material may be copied from original sources, even if referenced correctly, unless it is a direct quote indicated with quotation marks.
4. All work must be adequately and correctly referenced.
5. You should paraphrase (use your own words) the concepts that you are referencing, rather than quoting directly.
6. Marks will be awarded for the quality of your paraphrasing.
7. This is an open-book assessment.
8. Assessments must be typed unless otherwise specified.
9. Ensure that you save a copy of your responses.
9.1 Complete your responses in a Word document.
9.2 The document name must be your name.student number.Module Code.
9.3 Once you have completed the assessment, upload your document under the submission link in the correct module in Learn.
Additional instructions:
• Calculators are allowed.
• For multiple-choice questions, give only one (1) response per question. The marker will ignore any question with more than one answer, unless otherwise stated. You should, therefore, be sure of your answer before committing it to paper.
• Answer ALL Questions. .
• Show all calculations, where applicable (marks may be awarded for this).
If you are using a Word Document in specialised numeracy modules:
o Please see the Word document included as part of this assessment.
o Tables have been created for you to complete.
o Use the following to reflect your calculations:
o Multiple x – small letter x or *.
o Division / forward slash.
o Addition and subtraction + and -.
o Square roots and equations – using the function insert - equation.
o Tables – using the function insert – table.
o Working with tables – use merge and split cell functions through right click function.
o Fitting tables to pages – Autofit to window/content through right click function.
o Layout of table – Section breaks and landscape orientation through layout – breaks and layout orientation in the ribbon.
o If you are not familiar with all the functions in word it is recommended that you rather do a hardcopy if possible.
o The document name must be your name.student number.Module Code.
o
Once you have completed the assessment, upload your document under the submission link in the correct module in Learn.
Instructions for assessments including practical computer work:
o Use of good programming practice and comments in code is compulsory.
o Save your application in the location indicated by the administrator (e.g. the Z: drive or your local drive).
o Create a folder as follows: use the module code and your own student number and create a folder with a folder name as per the format shown here:
o StudentNumber_ModuleCode_Test. Save all files (including any source code files, template files, design files, image files, text files, database files, etc.) within this folder.
o E.g. if your student number is 12345 and you are writing an examination for the module QUAT6211, create a folder named 12345_QUAT6211_Test and use this throughout the session to save all of your files.
o
Important: Upon completion of your assessment, you must save and close all your open files and double click the ExamLog application on your desktop. You must follow the instructions carefully to ensure that the information about the files that you have submitted for this assessment has been logged on the network. Specify the location of your source code on your question paper.
Instructions for assessments including drawings in design qualifications:
o Drawings must be done on A3 paper and your name and student number must be included on all sheets.
o A 10mm border must be drawn around your drawing sheet and a title block must be inserted at the right-hand corner. Supply information as requested.
o Marks will be lost for poor planning and layout.
o Complete each of the questions on a separate page. Make use of various pencils, erasers and a viewfinder only.
o Draw all the required drawings on drawing paper as required.
o You may then scan or take a photo of the drawing for online submission.
Question 2 (Marks: 20)
Q.2.1 The Bookworm Club has found that 30% of its members attended school in the
Johannesburg area. A sample of 145 members is randomly selected. Assuming normal distribution:
Q.2.1.1 Determine the standard error for this sample. (3)
Q.2.1.2 What is the probability that more than 31.50% of the members of the club attended school in Johannesburg? Interpret your answer. (7)
Q.2.2 Experience has shown that on average, customers of the Cultured Camping website spend R750 (µ) per purchase, with a standard deviation of R85 (s). A sample of 95 purchases is randomly selected. Assuming normal distribution:
Q.2.2.1 Determine the standard error for this sample. (3)
Q.2.2.2 What is the probability that the mean value of the purchases in the sample is less than R755? Interpret your answer. (7)
Question 3 (Marks: 10)
Q.3.1 Of the 150 randomly selected mine workers interviewed, 28 indicated that they would prefer an industrial action if they did not get a 15% increase in their salaries.
Calculate a 95% confidence interval of the proportion of mine workers who would (10)
prefer an industrial action.
Question 4 (Marks: 20)
Q.4.1 Construct a 99% confidence interval for the true average number of hours that teenagers spend on social media per day, if it was found that the average number of hours that a sample of 22 teenagers spent on social media per day was 4.25 hours, with a standard deviation of 0.75 hours. (11)
Q.4.2 Construct a 90% confidence interval for the true average monthly cost of renting a one-bedroom flat in the Randpark Ridge area, if it was found that a sample of 110 different flats in the area cost an average of R5 999 per month. Assume a population standard deviation of R1 721.25. (9)
END OF PAPER

FORMULAE SHEET: Quantitative Techniques A and B
(QUAT5112 & QUAT6211)
1. Measures of central tendency
?? ??
( )
Median = ?? + Mode = ?? +
2. Measures of Dispersion
R = ?? - ?? ; R = upper limit of highest class – lower limit of lowest class
2 = ? ¯ s¯ s = v??
s

Interquartile range = Q3 - Q1 Quartile Deviation =
( ) ( ) cv = x 100% Skp = ; or Skp =
¯
?? = ?? + ?? = ?? +
P = lp + (Up – lp)((p/100)n – f( ))
fp
Where:
lp = lower class boundary of the interval containing the pth percentile Up = upper class boundary of the interval containing the pth percentile f( ) = cumulative frequency of the class interval before the interval containing the pth percentile
fp = frequency of the class interval containing the pth percentile
3. Probability distributions
P (r) = n C r prq(n-r)
Mean: µ = np
Standard deviation: ?? = ?????? where q = 1 – p
P (x) = For x = 0, 1, 2, 3,
!

Mean = a
Standard deviation = v??
4. Confidence Interval
?? ??
??¯ - ?? ¯
v?? v??

?? ?? ??¯ = ?? = ??¯ + ??
v?? v??

??(1 - ??) ??(1 - ??)
?? - ?? = ?? = ?? + ??
?? ??

(??¯ - ??¯ ) - ?? = ?? - ?? = ( ??¯

- ??¯ ) + ??

(??¯ - ??¯ ) - ?? = ?? - ?? = ( ??¯ - ??¯ ) + ??
(?? - ?? ) - ?? = ?? - ?? = ( ?? - ?? ) + ??
?? ?? ?? ??

5. Regression
?? = ?? + ?? ?? ???? ?? = ?? + ????
?? ?????? ??
6. Hypothesis testing
¯ ¯ ¯
?? or ?? = or ??
/v

( ¯ ¯ ) ( ) ( ¯ ¯ ) ( )
?? = , or ?? =
( ¯ ¯ ) ( ) ( ) ( ) ?? = , where ?? =
?? - ??
?? =
??(1 - ??)
??

?? = ( ) ( ) where ?? =
(?? -?? )
?? =
??

7. Index numbers
??
Price relative = × 100%
??

Laspeyres price index = × 100% Paasche price index = × 100%
8. Time series
Using the sequential numbering method (x = 1, 2, 3, 4, 5, …):
?? = ?? + ?? ??
Where: ?? ?????? ??
9. Linear Correlation
?? ??
10. Financial Mathematics
?? = ?? (1 + ????) ?? = ?? (1 + ??)
?? = ?? 1 + where k = number of compounding periods in a year.
?? = (1 + ) - 1 where m = number of compounding periods in a year
(1 + ??) - 1
?? = ??
??

1 - (1 + ??)
?? = ??
??

[(1 + ??) - 1](1 + ??)
?? = ??
??

[1 - (1 + ??) ](1 + ??)
?? = ??
??

1 - (1 + ??) ( ) 1 - (1 + ??)
?? = ?? -
?? ??

TABLE 3
This table gives the values of (df)(a)
Chi-square Distribution Table
d.f. .995 .99 .975 .95 .9 .1 .05 .025 .01
1 0.00 0.00 0.00 0.00 0.02 2.71 3.84 5.02 6.63
2 0.01 0.02 0.05 0.10 0.21 4.61 5.99 7.38 9.21
3 0.07 0.11 0.22 0.35 0.58 6.25 7.81 9.35 11.34
4 0.21 0.30 0.48 0.71 1.06 7.78 9.49 11.14 13.28
5 0.41 0.55 0.83 1.15 1.61 9.24 11.07 12.83 15.09
6 0.68 0.87 1.24 1.64 2.20 10.64 12.59 14.45 16.81
7 0.99 1.24 1.69 2.17 2.83 12.02 14.07 16.01 18.48
8 1.34 1.65 2.18 2.73 3.49 13.36 15.51 17.53 20.09
9 1.73 2.09 2.70 3.33 4.17 14.68 16.92 19.02 21.67
10 2.16 2.56 3.25 3.94 4.87 15.99 18.31 20.48 23.21
11 2.60 3.05 3.82 4.57 5.58 17.28 19.68 21.92 24.72
12 3.07 3.57 4.40 5.23 6.30 18.55 21.03 23.34 26.22
13 3.57 4.11 5.01 5.89 7.04 19.81 22.36 24.74 27.69
14 4.07 4.66 5.63 6.57 7.79 21.06 23.68 26.12 29.14
15 4.60 5.23 6.26 7.26 8.55 22.31 25.00 27.49 30.58
16 5.14 5.81 6.91 7.96 9.31 23.54 26.30 28.85 32.00
17 5.70 6.41 7.56 8.67 10.09 24.77 27.59 30.19 33.41
18 6.26 7.01 8.23 9.39 10.86 25.99 28.87 31.53 34.81
19 6.84 7.63 8.91 10.12 11.65 27.20 30.14 32.85 36.19
20 7.43 8.26 9.59 10.85 12.44 28.41 31.41 34.17 37.57
22 8.64 9.54 10.98 12.34 14.04 30.81 33.92 36.78 40.29
24 9.89 10.86 12.40 13.85 15.66 33.20 36.42 39.36 42.98
26 11.16 12.20 13.84 15.38 17.29 35.56 38.89 41.92 45.64
28 12.46 13.56 15.31 16.93 18.94 37.92 41.34 44.46 48.28
30 13.79 14.95 16.79 18.49 20.60 40.26 43.77 46.98 50.89
32 15.13 16.36 18.29 20.07 22.27 42.58 46.19 49.48 53.49
34 16.50 17.79 19.81 21.66 23.95 44.90 48.60 51.97 56.06
38 19.29 20.69 22.88 24.88 27.34 49.51 53.38 56.90 61.16
42 22.14 23.65 26.00 28.14 30.77 54.09 58.12 61.78 66.21
46 25.04 26.66 29.16 31.44 34.22 58.64 62.83 66.62 71.20
50 27.99 29.71 32.36 34.76 37.69 63.17 67.50 71.42 76.15
55 31.73 33.57 36.40 38.96 42.06 68.80 73.31 77.38 82.29
60 35.53 37.48 40.48 43.19 46.46 74.40 79.08 83.30 88.38
65 39.38 41.44 44.60 47.45 50.88 79.97 84.82 89.18 94.42
70 43.28 45.44 48.76 51.74 55.33 85.53 90.53 95.02 100.43
75 47.21 49.48 52.94 56.05 59.79 91.06 96.22 100.84 106.39
80 51.17 53.54 57.15 60.39 64.28 96.58 101.88 106.63 112.33
85 55.17 57.63 61.39 64.75 68.78 102.08 107.52 112.39 118.24
90 59.20 61.75 65.65 69.13 73.29 107.57 113.15 118.14 124.12
95 63.25 65.90 69.92 73.52 77.82 113.04 118.75 123.86 129.97
100 67.33 70.06 74.22 77.93 82.36 118.50 124.34 129.56 135.81