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Elementary Statistics
Assignment 1 Question Paper
Guideline
• Prepare A4 sized papers or single-lined papers as answer sheets. You may use more than one page.
• Write down your name and student ID on page 1 of your answer sheets.
• Your solution must be handwritten on papers. Electronic file created from iPad / tablet device is not accepted. Typed solution is not accepted.
• All assignments are individual works. Keep your original hardcopy for checking.
• Scan your finished assignment as a single pdf file with file size less than 100 MB (no other file format is accepted). The file should be named as “Student Name_ES_A1.pdf”, e.g. “Chan Tai Man_ES_A1.pdf”
• Submit your pdf document to SOUL class link before 1 March (Friday) 23:59. Mark deduction will be applied for late submission as follow:
Submission on 2 March (Saturday): -20%
Submission on 3 March (Sunday): -50%
Submission on or after 4 March (Monday): 0 mark
• After submission, click the submitted file and check:
i. you have successfully submitted the correct file
ii. your writing is clear
iii. all pages are included
iv. the file can be opened properly by Acrobat Reader
It is student’s responsibility to do all necessary checking.
File cannot be opened / read / submission of wrong file will be scored 0 mark.
• Your submission date and time will be recorded in the system. Any change / checking must be made before deadline. Changes made / resubmission of file after deadline would be recorded as late.
• There are several mobile apps for scanning document to pdf file. You may try Adobe Scan / Office Lens / …
• For any question / sick leave application, please contact your class lecturer (contact email can be found in class link) before 1 March, 5:00p.m. Medical certificate / supporting document must be submitted for sick leave application.
Full marks: 30 marks
Show your calculation. Correct your answer to 4 decimal places when applicable.
Question 1 (12 marks)
A bank located in a residential area is concerned about the peak hour service between noon and 2:00PM. The waiting time, in minutes, has been collected from a sample of 15 customers during the peak hour.
9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35
10.49 6.68 5.64 4.08 6.17 9.91 5.47
(a) Compute the mean, standard deviation and range.
(b) The bank would like to use an AI machine to shorten the waiting time to enhance the service provided. The vendor claims that their AI machine would shorten waiting times by 15% on average after on-site testing in a bank. Is it possible to have the average waiting time not to exceed 5 minutes? Please state your reason(s).
(c) Classify the sampling method in the following cases.
(i) The 8th customer entering the bank and every 20th customer thereafter was asked to indicate the number of credit cards in his/her wallet.
(ii) Researchers divided the customers into six groups according to gender (male or female) and monthly income group (high, medium or low). 2% of customers from each group were selected and interviewed to determine if he/she applied personal loan in the last year.
(d) Referring to part (c), state whether the data collected (which are underlined) is numerical or categorical variable and further indicate it is discrete, continuous, nominal, or ordinal.
Question 2 (18 marks)
An engineering program has 130 students who are currently Year 2 students. Only 13 students are
selected to participate in the overseas study tour.
(a) A unique number is assigned to each of the students, from 001 to 130. Suppose the candidate is selected by systematic sampling method and the student with number 007 is selected. Write down the next 3 student numbers who are selected to join the tour.
(b) After completing the study tour, they are required to submit the assignment to fulfil the graduation requirements.
The following are the results of the assignment (in marks):
54 22 25 23 36 43 7 43 25 47 24 45 44
(i) Find the Q1, Q2 , Q3 and interquartile range.
(ii) The passing mark of this assignment is 40. The lecturer would like to adjust each student's mark so that half of them would pass the test. Use N be the original mark (before adjustment) and F be the final mark (after adjustment). If the mark is adjusted by the formula F = 0.95N + a , what is the value of a so that the median of final mark is 40.
(iii) Hence, find the Q1 and interquartile range of final mark.