low is the extract of the first few questions in the questionnaire. Define the type of variable (Numerical Discrete / Numerical Continuous / Categorical Nominal / Categorical Ordinal) for each of the variables: QI: Your studying program Circle your answer: Business / Engineering / Arts / Science) QII: Traveling time from home to college on 20 February 2022 (in minutes): __________ QIII:Total spending on meal (breakfast + lunch + dinner) on 20 February 2022 (Circle your answer: Below $40 / $40 – less than $80 /
Question 1
A student project has involved a survey about the spending habits of students in a college.
(a) Below is the extract of the first few questions in the questionnaire. Define the type of variable (Numerical Discrete / Numerical Continuous / Categorical Nominal / Categorical Ordinal) for each of the variables:
QI: Your studying program
Circle your answer: Business / Engineering / Arts / Science)
QII: Traveling time from home to college on 20 February 2022 (in minutes): __________
QIII:Total spending on meal (breakfast + lunch + dinner) on 20 February 2022
(Circle your answer: Below $40 / $40 – less than $80 / $80 – less than $120 / $120 or above)
QIV: Number of T-shirts you’ve bought in January 2022: _______________
A student in the team suggested the following sampling procedure:
“We target to interview 40 students. As all college students (1000 students) will attend college assembly on every Monday morning at 9 am, let’s arrange our interview at the College Entrance (there is only one entrance at the College) from 8 am, the time that the school entrance opens on the coming Monday. We can invite student as interviewee for every fixed number student entering the college.”
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(b) What is the name this sampling method?
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(c) Find the fixed number mentioned by this student.
(d) If, by using a random number generator, the 12th student entering the college should be the first interviewee. Write down who should be the second, the third and the sixth interviewees.
Question 2
In an inter-school competition, there are a total of 14 participants. Each participant answered 20 multiple choice questions. Below are the number of correct answers obtained by the participants:
16, 11, 20, 19, 18, 17, 15, 16, 17, 19, 20, 17, 13, 13
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(a) Find the mean, 90th percentile,
interquartile range , and standard deviation of the number of correct answers obtained by a participant. -
(b) Each participant has a basic score of 100 points. For each correct answer, 20 points would be given; for each wrong answer, 10 points would be deducted. Use X to represent the number of correct answers and Y to represent the final points of the participant, express Y as a linear
function of X. -
(c) Find the following summary statistics of the final points a participant gets in this competition: Mean, standard deviation, interquartile range, maximum.
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(d) Write a simple summary report (in around 30 – 50 words) about the final points of a participant gets in this inter-school competition. (The summary report needs to include all summary statistics found in part (c)).
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